Toward elucidating infrared dynamics of chiral gauge theories, we reevisit the vacuum structure of an $\mathrm{SU}(6)$ model from the viewpoint of the 't~Hooft anomaly matching.
For this purpose, we identify 't~Hooft anomalies in the UV theory
using the Stora-Zumino procedure.
Subsequently, we construct an effective theory
by applying the idea of the Wess-Zumino-Witten action to derive the topological terms
that encode the 't Hooft anomalies.
We also demonstrate that a low-energy effective theory
reproducing a part of the anomalies is described by a $\mathbb{z}_ 3$-valued scalar field.