Automorphism group of $\Bbb Z\times \Bbb Z \times \Bbb Z$ is $SL(3,\Bbb Z)$. I am wondering what the automorphism group of $(\Bbb Z\times \Bbb Z) \rtimes \Bbb Z$ would be. Lets say the generators of the three $\Bbb Z$s in $(\Bbb Z\times \Bbb Z) \rtimes \Bbb Z$ are $a,b,$ and $c$ respectively. $c$ acts on $a$ and $b$ as, $cac^{-1}=b^{-1}; cbc^{-1}=a$. thanks