Your public key contains two numbers. First it is a number n, which is called the Modulus and are computed through $p \cdot q = n$.
The second number is e, which is the public exponent and are used to encrypt your message m. The number e is choosen that it have the following properties:
\begin{equation}
1 < e < \phi(n) = (p-1)(q-1)
\end{equation}
\begin{equation}
gcd(e, (p-1)(q-1)) = 1
\end{equation}
$\phi$ is the euler's totient function.
The private key contains the numbers p,q and d. The number d is your private exponent and p,q are your prime numbers, which helps you do calculate n and the private and public exponent.
The private exponent have the following properties:
\begin{equation}
1 < d < (p-1)(q-1)
\end{equation}
\begin{equation}
d = e^{-1} mod~(p-1)(q-1)
\end{equation}
I am not sure, what are Dp, Dq and QInv in your configuration is, but if you have d you are able to compute e with:
\begin{equation}
e = d^{-1} mod~(p-1)(q-1)
\end{equation}
I hope it will help you. If that doesn't help may specifiy what are Dp, Dq and QInv are.
EDIT:
I think you are using the PKCS#1, which are mentioned in the comments below of this answer.
In the PKCS#1 you are also able to have a quintuple as a private key, which are p, q, Dp, Dq and QInv.
Dp and Dq satisfy the following equations:
\begin{equation}
e \cdot Dp \equiv 1~mod~(p-1) \Leftrightarrow e = Dp^{-1} ~mod ~(p-1) \\
e \cdot Dq \equiv 1~mod~(q-1) \Leftrightarrow e = Dq^{-1} ~mod ~(q-1)
\end{equation}
and the number e have a little bit different property.
The property of e is:
\begin{equation}
gcd(e, \lambda(n)) = 1~and~\lambda(n) = LCM(p,q)
\end{equation}
Additionally your d is satisfying this equation instead of that from above:
\begin{equation}
ed \equiv 1 ~mod ~\lambda(n) \Leftrightarrow e = d^{-1} ~mod ~\lambda(n)
\end{equation}
This equation should give you the right e from your giving d and $e = d^{-1}~mod~\lambda(n)$ means compute the modular inverse from d with the modulus $LCM(p,q)$.
I hope this will help you.
