I'm reading David R. Finston and Patrick J. Morandi's book Abstract Algebra: Structure and Application and in its last section 10.6 "the 17 wallpaper groups" page 179 I'm confused on what it gives as an example of $pmg$:
According to its description on pg 178, $pmg$ has point group $D_2$ , so it shall contains a rotation. Wikipage on pmg also says so:
"The group pmg has two rotation centres of order two (180°), and reflections in only one direction. It has glide reflections whose axes are perpendicular to the reflection axes. The centres of rotation all lie on glide reflection axes."
But I couldn't find a rotation here in the pattern.
So, where did I miss?
Update for Doug’s answer:
If takes the red dot as the rotation centre, the two blue parts don’t match:
You can rotate at the intersection points of $4$ tiles by $180$ degrees. There are two kinds of intersections points depending on whether say the upper right is white or grey.