What class of elements makes up the groups on the right side of the periodic table?
These elements are generally non-metals, and consist of ten gases (eleven if you count #118), one liquid and the rest solids at room temperature.
Aside from the fact all are non-metals, there is not a lot of other similarity among the columns on the right of the table.
The groups include the noble gases on the extreme right - a family of non-reactive gases. Next to them are the halogens, a collection of highly reactive and very electronegative (electron-seeking) non-metals. The name means "salt-forming" as this is what they do on reacting with metals - they produce salts (ionic solids).
The next column to the left of the halogens is the chalcogens, which include oxygen and sulfur as familiar examples.