# Locally-Dihedral 2-group

Let $Z_{2^{\infty}}$ be 2-prufer group. I want to define $G=Z_{2^{\infty}}$semi-direct $ b$ =$<$$a$$,b|b^2=1,b^{-1}ab=a^{-1} $, for $a$ $\in A>$ in sage. I think this is possible in GAP but I don't know how to define?