  In this article, we focus on the left (translation) actions on noncommutative
compact connected Lie groups ${\rm SU}(2) \times T^n$. We define the rotation
vectors of the left actions induced by the elements in the maximal tori of
${\rm SU}(2) \times T^n$, and utilize rotation vectors to give the complete
topologically conjugate classifications of left actions. Algebraic conjugacy
and smooth conjugacy are also considered.
