deconfinement phase transition to the true deconfined quark-gluon plasma. The hadronic density of states for the discrete low-lying mass spectrum is found from the available ex- perimental data that is listed in the particle data group book [3]. The discrete low-lying mass spectrum is extrapolated to the continuous high-lying one using reasonable theoret- ical models. The standard theoretical procedure to find the hadronic density of states is carried out by computing the micro-canonical ensemble for the quark and gluon bag with specific internal symmetry that is consistent with the experimental observation and other theoretical models. The confined quark and gluon state is guaranteed by projecting the color-singlet state (i.e. the colorless state). The structure of the underlying internal color symmetry of a composite bag has attracted much attention in order to understand the con- finement/deconfinement in QCD. The Hagedorn model seems to be very useful in studying the shear viscosity of QGP and even investigating the extended gauge (conformal) field theories such as AdS/CFT. The bag’s constituent quarks and gluons are considered in the context of various underlying symmetry groups such as the orthogonal, unitary and sym- plectic symmetry groups as well as U (1) N$_{c}$ symmetry group. In order to be consistent with QCD, the unimodular-like constraint is imposed in the all symmetry groups those are under the present investigation. The unimodular-like constraint is an additional constraint for the orthogonal and symplectic symmetry groups and its absence does not affect the general discussion of the present work. Usually, the natural choice in QCD is the unitary symme- try group. Hence, the transmutation from the unitary symmetry group to orthogonal or symplectic symmetry group is associated with a new phenomenology. The major argument is that: is it possible under certain scenario the the Hagedorn matter that is dominated by the colorless unitary states to be altered (by transmutation) to another one dominated by either colorless orthogonal states or colorless symplectic ones and vice versa? It is im- portant to mention here that the Hagedorns are colorless regardless of their internal color symmetries. The colorless is guaranteed by projecting the color-singlet-state. The answer is that: this scenario seems to be reasonable in order to explain the elusive behaviour of the deconfinement quark gluon plasma in the phase transition diagram. Furthermore, the relevant point to the hadronic phase transition is the Gross-Witten point. This point is associated by modifications in the hadronic matter properties. The Gross-Witten point is strongly believed to be not the deconfinement point and to be merely a transition from hadronic matter that is known to be dominated by the low-lying mass 44