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Based on the neutron and proton degrees of freedom, the low-lying energylevels, the $E2$, $M1$ and $E0$ transition strengths of nucleus $^{124}$Te havebeen calculated by the neutron-proton interacting boson model. The calculatedresults are quite consistent with the experimental data. By comparing the keyobservables of states at the critical point of $\textrm{U}_{\pi\nu}(5)$--$\textrm{O}_{\pi \nu}(6)$ transition with experimental data andcalculated results, we show that the $^{124}$Te is a possible nucleus at thecritical point of the second order phase transition from vibration to unstablerotation and such a critical point contains somewhat triaxial rotation. The0$^+_2$ state of $^{124}$Te can be interpreted as the lowest state of the firstexcited family of intrinsic levels in the critical point symmetry.

Description of the critical point symmetry in 124Te by IBM-2