  It was shown [Chin. Phys. Lett. 28, 020503 (2011)] that at zero temperature
the ground state of the one-dimensional (1D) $w$-component Fermi gas coincides
with that of the spinless Bose gas in the limit $\omega\to \infty$. This
behaviour was experimentally evidenced through a quasi-1D tightly trapping
ultracold ${}^{173}$Yb atoms in the recent paper [Nature Physics 10, 198
(2014)]. However, understanding of low temperature behaviour of the Fermi gases
with a repulsive interaction acquires spin-charge separated conformal field
theories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic
$SU(w)$ Heisenberg spin chain. Here we analytically derive universal
thermodynamics of 1D strongly repulsive fermionic gases with $SU(w)$ symmetry
via the Yang-Yang thermodynamic Bethe ansatz method. The analytical free energy
and magnetic properties of the systems at low temperatures in a weak magnetic
field are obtained through the Wiener-Hopf method. In particular, the free
energy essentially manifests the spin-charge separated conformal field theories
for the high symmetry systems with arbitrary repulsive interaction strength. We
also find that the sound velocity of the Fermi gases in the large $w$ limit
coincides with that for the spinless Bose gas, whereas the spin velocity
vanishes quickly as $w$ becomes large. This indicates a strong suppression of
the Fermi exclusion statistics by the commutativity feature among the
$w$-component fermions with different spin states in the Tomonaga-Luttinger
liquid phase. Moreover, the equations of state and critical behaviour of
physical quantities at finite temperatures are analytically derived in terms of
the polylogarithm functions in the quantum critical region.
