  We investigate the onset of chaos in a periodically kicked Dicke model (KDM),
using the out-of-time-order correlator (OTOC) as a diagnostic tool, in both the
oscillator and the spin subspaces. In the large spin limit, the classical
Hamiltonian map is constructed, which allows us to investigate the
corresponding phase space dynamics and to compute the Lyapunov exponent. We
show that the growth rate of the OTOC for the canonically conjugate coordinates
of the oscillator is able to capture the Lyapunov exponent in the chaotic
regime. The onset of chaos is further investigated using the saturation value
of the OTOC, that can serve as an alternate indicator of chaos in a generic
interacting quantum system. This is also supported by a system independent
effective random matrix model. We further identify the quantum scars in KDM and
detect their dynamical signature by using the OTOC dynamics. The relevance of
the present study in the context of ongoing cold atom experiments is also
discussed.
