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We present the photometric and spectroscopic evolution of the type Ic supernova LSQ14efd, discovered by the La SillaQUEST survey and followed by PESSTO. LSQ14efdwas discovered fewdays after explosion and the observations cover up to ~100 d. The early photometric points show the signature of the cooling of the shock break-out event experienced by the progenitor at the time of the supernova explosion, one of the first for a type Ic supernova. A comparison with type Ic supernova spectra shows that LSQ14efd is quite similar to the type Ic SN 2004aw. These two supernovae have kinetic energies that are intermediate between standard Ic explosions and those which are the most energetic explosions known (e.g. SN 1998bw).We computed an analytical model for the light-curve peak and estimated the mass of the ejecta 6.3 ± 0.5 M⊙, a synthesized nickel mass of 0.25 M⊙ and a kinetic energy of Ekin = 5.6 ± 0.5 × 1051 erg. No connection between LSQ14efd and a gamma-ray burst event could be established. However we point out that the supernova shows some spectroscopic similarities with the peculiar SN-Ia 1999ac and the SN-Iax SN 2008A. A core-collapse origin is most probable considering the spectroscopic, photometric evolution and the detection of the cooling of the shock breakout. [ABSTRACT FROM AUTHOR]