  Discrete Floquet time crystals (DFTC) are characterized by the spontaneous
breaking of the discrete time-translational invariance characteristic of
Floquet driven systems. In analogy with equilibrium critical points, also
time-crystalline phases display critical behaviour of different order, i.e.,
oscillations whose period is a multiple $p > 2$ of the Floquet driving period.
Here, we introduce a new, experimentally-accessible, order parameter which is
able to unambiguously detect crystalline phases regardless of the value of $p$
and, at the same time, is a useful tool for chaos diagnostic. This new paradigm
allows us to investigate the phase diagram of the long-range (LR) kicked Ising
model to an unprecedented depth, unveiling a rich landscape characterized by
self-similar fractal boundaries. Our theoretical picture describes the
emergence of DFTCs phase both as a function of the strength and period of the
Floquet drive, capturing the emergent $\mathbb{Z}_p$ symmetry in the
Floquet-Bloch waves.
