The point group generator allows you to build a point group of your Bravais lattice. 2.5
How does the generator work? The generator first checks the point symmetry of the Bravais lattice (``YOUR CRYSTAL CLASS GROUP IS ...'') and then each operation of this group is applied to every atom in the cell. In this way, an actual point group is built (``YOUR LARGEST SYMMORPHIC GROUP IS ...'') and shown (the name of the group and all the elements as shown in Figs. 2.1 and 2.2). A menu which opens up here allows you to either adopt this group (``ADOPT THE LARGEST SYMMORPHIC GROUP''), continue generation of the group by adding new elements from the crystal class group (``PROCEED GENERATION FROM'') or start generation from scratch. In the last two cases you can add/remove elements, the generator multiplies all the elements with each other, adds new elements (if necessary) and then shows you the current group generated so far.
If the symmetry and/or special constraints imposed on atomic coordinates have not been used at the stage of atomic relaxation while running a DFT code, the symmetry generator may fail to determine the correct symmetry group due to numerical errors in the atomic positions. Therefore, to make your symmetry group as rich as possible, you may need to generate the symmetry manually. One method is to use the geometry of the unrelaxed system (if it should have the same symmetry). Other (brr!!!) would be to edit your geometry file to make sure that there is no any numerical noise in the atomic coordinates (in some cases this is a real challenge!). Alternatively, use the point group generator: it allows you to play with the symmetry operations by adding/removing them, each time the whole group is generated and shown. It is a useful exercise in the group theory as well, especially in understanding group generators.