= Solution
\b[There are $2_1$ <screw axes> parallel to $[100]$ through $(y/b,z/c)=(1/4,0),(3/4,0),(1/4,1/2),(3/4,1/2)$], with periodic repeats.
For the first axis the operation in fractional coordinates is
$$
(x,y,z)\longmapsto(x+1/2,1/2-y,-z).
$$
It rotates by $180^\circ$ about the axis and translates by $a/2$. For example, it sends the A center at $(0,0,0)$ to the A center at $(1/2,1/2,0)$, and sends B at $(1/2,0,1/2)$ to B at $(0,1/2,1/2)$ modulo integer translations. A half-turn preserves each unoriented diatomic bond. A second application gives one full $a$ translation.
There are also ordinary twofold axes through the molecular-center rows; those should not be confused with the <screw axes> halfway between the corresponding rows.
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