Space groups: Herman-Maugin notation, diagrams and Wyckoff positions
Well, knowing crystallography implies being able to deduce the picture above solely from the group's name $\rm Pmab$, and that's how it is done.

First you write down the symmetry elements mentioned explicitly in the group's name (that is, $\rm m,\;a$, and $\rm b$ in our case; in other examples there could have been axes among them, or even worse) and orient those accordingly, which you already know how to do. Then you combine these elements in all possible ways to find out what else is hidden beneath.

Essentially, any symmetry element is but a linear transformation that takes any vector $\bf\vec x$ to another vector $\bf A\vec x+\vec b$, where $\bf A$ is the $3\times3$ matrix of our transformation (rotation or reflection or otherwise), and $\bf\vec b$ is the shift, that is, a half-translation along the axis for a screw axis, or a half-translation in whatever direction for a glide plane, or $\bf\vec0$ in all other cases. The typical matrices are:
$$
\begin{array}{cc}
\begin{pmatrix}
-1 &amp; 0 &amp; 0 \\
0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 1 \\
\end{pmatrix} &amp;
\begin{pmatrix}
1 &amp; 0 &amp; 0 \\
0 &amp; -1 &amp; 0 \\
0 &amp; 0 &amp; -1 \\
\end{pmatrix}&amp;
\begin{pmatrix}
-1 &amp; 0 &amp; 0 \\
0 &amp; -1 &amp; 0 \\
0 &amp; 0 &amp; -1 \\
\end{pmatrix}\\
\text{Reflection $\perp$ X} &amp; \text{Rotation about X}&amp; \text{Center}
\end{array}
$$

Given two symmetry elements, you simply combine the two transformations by doing some matrix multiplication, which I sincerely recommend, if only to know how it feels. Alternatively, you may rely upon the wisdom of the predecessors, which says:


Two perpendicular planes give a twofold axis parallel to both.
A plane and a parallel twofold axis give another plane, perpendicular to the plane and parallel to the axis.
A plane and a perpendicular twofold axis give a center.
Two perpendicular twofold axes give a third axis, perpendicular to both.
All of the above remains true if you change


every "plane" to "plane or a glide plane" and
every "axis" to "axis or a screw axis".

When some of the combined elements have shift in them, the following happens:


If the shift is parallel to the resulting element, it becomes a part of the said element (that is, the result is going to be a screw axis or a glide plane).
If the shift is perpendicular to the resulting element, it moves the said element by half the value of the shift (that is, by $1\over4$ of a translation).

If you end up with a center of symmetry someplace other than at the origin, you relocate your origin there.


Now try to apply the rules 1-7 and see where this gets you.