  Let $M=Q(i\sqrt{d})$ be any imaginary quadratic field with a positive
square-free $d$. Consider the polynomial \[ f(x)=x^3-ax^2-(a+3)x-1, \] with a
parameter $a\in Z$. Let $K=M(\alpha)$, where $\alpha$ is a root of $f$. This is
an infinite parametric family of sextic fields depending on two parameters, $a$
and $d$. Applying relative Thue equations we determine the relative power
integral bases of these sextic fields over their quadratic subfields. Using
these results we also determine generators of (absolute) power integral bases
of the sextic fields.
