  Based on the neutron and proton degrees of freedom, the low-lying energy
levels, the $E2$, $M1$ and $E0$ transition strengths of nucleus $^{124}$Te have
been calculated by the neutron-proton interacting boson model. The calculated
results are quite consistent with the experimental data. By comparing the key
observables of states at the critical point of $\textrm{U}_{\pi
\nu}(5)$--$\textrm{O}_{\pi \nu}(6)$ transition with experimental data and
calculated results, we show that the $^{124}$Te is a possible nucleus at the
critical point of the second order phase transition from vibration to unstable
rotation and such a critical point contains somewhat triaxial rotation. The
0$^+_2$ state of $^{124}$Te can be interpreted as the lowest state of the first
excited family of intrinsic levels in the critical point symmetry.
