Automorphism group of the quanternion group

The quaternion group is the group $Q$ generated by the complex matrices

\[A = \begin{pmatrix} 0 & 1\\ -1 & 0\\ \end{pmatrix}, \qquad B = \begin{pmatrix} 0 & i\\ i & 0\\ \end{pmatrix}.\] \[I=\begin{pmatrix}1&0\\0&1\end{pmatrix},\quad A=\begin{pmatrix}0&1\\-1&0\end{pmatrix},\quad B=\begin{pmatrix}0&i\\ i&0\end{pmatrix},\quad AB=\begin{pmatrix}i&0\\0&-i\end{pmatrix}.\]