  We designed a quantum circuit to prepare a permutation-symmetric maximally
entangled three-qubit state called the $\vert {\rm S} \rangle$ state and
experimentally created it on an NMR quantum processor. The presence of
entanglement in the state was certified by computing two different entanglement
measures, namely negativity and concurrence. We used the $\vert {\rm S}
\rangle$ state in conjunction with a set of maximally incompatible local
measurements, to demonstrate the maximal violation of inequality number $26$ in
Sliwa's classification scheme, which is a tight Bell inequality for the (3,2,2)
scenario i.e. the three party, two measurement settings and two measurement
outcomes scenario.
