  We investigate the properties of low angular momentum, relativistic, viscous,
advective accretion flows around rotating black holes that include shock waves
in the presence of thermal conduction. We self-consistently solve the governing
fluid equations to obtain the global transonic accretion solutions for a set of
model parameters, namely energy ($\mathcal{E}$), angular momentum ($\lambda$),
viscosity ($\alpha$), conduction parameter ($\Phi_{\rm s}$) and cooling
parameter ($f_{\rm c}$). We observe that depending on the model parameters,
accretion flow experiences centrifugally supported shock transition and the
present study, for the first time, focuses on examining the shock properties,
such as shock radius ($r_{\rm s}$), compression ratio ($R$) and shock strength
($\Psi$) regulated by the dissipation parameters ($\Phi_{\rm s},~f_{\rm c}$).
We show that shock-induced global accretion solutions persist for wide range of
model parameters and identify the boundary of the parameter space in
energy-angular momentum plane that admits standing shocks for different
dissipation parameters ($\Phi_{\rm s},~f_{\rm c}$). Finally, we compute the
critical conduction parameter ($\Phi_{\rm s}^{\rm cri}$), beyond which shock
ceases to exist. We find that $\Phi_{\rm s}^{\rm cri}$ directly depends on the
black hole spin ($a_{\rm k}$) with $\Phi_{\rm s}^{\rm cri} \sim 0.029$ and
$\sim 0.04$ for weakly ($a_{\rm k}\rightarrow 0$) and rapidly ($a_{\rm
k}\rightarrow 1$) rotating black hole. Furthermore, we observe that $\Phi_{\rm
s}^{\rm cri}$ decreases with increasing viscosity ($\alpha$), and shocked
accretion solutions continue to exist for $\alpha \lesssim 0.065$ ($a_{\rm k}
\rightarrow 0$) and $\lesssim 0.104$ ($a_{\rm k} \rightarrow 1$), respectively.
