  We have analytically calculated the quantum discord for a system composed of
spin-$j$ and spin-1/2 subsystems possessing SU(2) symmetry. We have compared
our results with the quantum discord of states having similar symmetries and
seen that in our case amount of quantum discord is much higher. Moreover, using
the well known entanglement properties of these states, we have also compared
their quantum discord with entanglement. Although the system under
consideration is separable nearly all throughout of its parameter space as $j$
increases, we have seen that discord content remains significantly large.
Investigation of quantum discord in SU(2) invariant states may find application
in quantum computation protocols that utilize quantum discord as a resource
since they arise in many real physical systems.
