  In this note we present examples of complex algebraic surfaces with canonical
maps of degree $12$, $13$, $15$, $16$ and $18$. They are constructed as
quotients of a product of two curves of genus $10$ and $19$ using certain
non-free actions of the group $S_3\times \mathbb Z_3^2$. To our knowledge there
are no other examples in literature of surfaces with canonical map of degree
$13$, $15$ and $18$.
