  A Poisson algebra $\Bbb C[G]$ considered as a Poisson version of the twisted
quantized coordinate ring $\Bbb C_{q,p}[G]$, constructed by Hodges, Levasseur
and Toro in \cite{HoLeT}, is obtained and its Poisson structure is
investigated. This establishes that all Poisson prime and primitive ideals of
$\Bbb C[G]$ are characterized. Further it is shown that $\Bbb C[G]$ satisfies
the Poisson Dixmier-Moeglin equivalence and that Zariski topology on the space
of Poisson primitive ideals of $\Bbb C[G]$ agrees with the quotient topology
induced by the natural surjection from the maximal ideal space of $\Bbb C[G]$
onto the Poisson primitive ideal space.
