TABLE I: The mass spectral exponent α which appears in ρ$_{(}$$_{II}$$_{)}$ = cm − $^{α}$eb m for the color-singlet state bag (i.e. Hagedorn state) versus the bag’s internal symmetry that is given by the U (1) $^{N$_{c}$}$, orthogonal O ( N$_{c}$ ), unitary U ( N$_{c}$ ) and symplectic Sp ( N ) ( N = N$_{c}$ ) symmetry groups and they are restricted to the unimodular-like constraint. The exponent α for the color-non-singlet quark-gluon bags (i.e. colored SU ( N$_{c}$ )) state is included. Symmetry group α ( N$_{c}$ ) α ( N$_{c}$ = 3) Non-singlet SU ( N$_{c}$ ) state (not Hagedorn state): 1 2 1 2 Color-singlet unimodular-like U (1) $^{N$_{c}$}$: 1 $_{2}$N$_{c}$ 3 2 Color-singlet unimodular-like orthogonal O$_{(}$$_{S}$$_{)}$ ( N$_{c}$ ): 1 4 ( N 2 c + N$_{c}$ ) 3 Color-singlet unimodular-like unitary U ( N$_{c}$ ): 1 $_{2}$N 2 c 9 2 Color-singlet unimodular-like symplectic Sp ( N$_{c}$ ): N 2 c − 1 $_{2}$N$_{c}$ 15 2 65