The twisted Alexander polynomial is an invariant of a knot with a finite dimensional representation. For example, a homomorphism from the knot group to a finite group yields a twisted Alexander polynomial via the regular representation. Friedl and Vidussi proved that every non-fibered knot admits an epimorphism onto a finite group with vanishing twisted Alexander polynomial, and we call the least order of such finite groups the twisted Alexander vanishing (TAV) order. In this talk, after reviewing the definition of the twisted Alexander polynomial, we show some examples and properties of TAV order.