  We consider the family
  $\mathcal{E}(s,r,d)=\Big\{ X(z)=\frac{Q(z)}{P(z)}\ e^{E(z)}
\frac{\partial}{\partial z} \Big\},$
  with $Q, P, E$ polynomials, deg${Q}=s$, deg$(P)=r$ and deg$(E)=d$, of
singular complex analytic vector fields $X$ on the Riemann sphere
$\widehat{\mathbb{C}}$. For $d\geq1$, $X\in\mathcal{E}(s,r,d)$ has $s$ zeros
and $r$ poles on the complex plane and an essential singularity at infinity.
Using the pullback action of the affine group $Aut(\mathbb{C})$ and the
divisors for $X$, we calculate the isotropy groups $Aut(\mathbb{C})_{X}$ and
the discrete symmetries for $X\in\mathcal{E}(s,r,d)$. Each subfamily
$\mathcal{E}(s,r,d)_{id}$, of those $X$ with trivial isotropy group in
$Aut(\mathbb{C})$, is endowed with a holomorphic trivial principal
$Aut(\mathbb{C})$-bundle structure. Necessary and sufficient conditions in
order to ensure the equality $\mathcal{E}(s,r,d)=\mathcal{E}(s,r,d)_{id}$ and
those $X\in\mathcal{E}(s,r,d)$ with non-trivial isotropy are realized. Explicit
global normal forms for $X\in\mathcal{E}(s,r,d)$ are presented. A natural
dictionary between vector fields, 1-forms, quadratic differentials and
functions is extended to include the presence of non-trivial discrete
symmetries $\Gamma<Aut(\mathbb{C})$.
