In this talk I will discuss the existence of time-translation symmetry breaking in a kicked infinite-range-interacting clean spin system described by the Lipkin-Meshkov-Glick model. This Floquettime-crystal is robust under perturbations of the kicking protocol, its existence being intimatelylinked to the underlying Z2 symmetry breaking of the time-independent model. I will show thatthe model being infinite-range and having an extensive amount of symmetry breaking eigenstatesis essential for having the time-crystal behaviour. In particular I will discuss the properties of theFloquet spectrum, and show the existence of doublets of Floquet states which are respectivelyeven and odd superposition of symmetry breaking states and have quasi-energies differing of halfthe driving frequencies, a key essence of Floquet time-crystals. Remarkably, the stability of thetime-crystal phase can be directly analysed in the limit of infinite size, discussing the propertiesof the corresponding classical phase space.