The groups object may be used to access examples of various groups. Using tab-completion on this object is an easy way to discover and quickly create the groups that are available (as listed here).
Let <tab> indicate pressing the tab key. So begin by typing groups.<tab> to the see primary divisions, followed by (for example) groups.matrix.<tab> to access various groups implemented as sets of matrices.
Miscellaneous Groups (groups.misc.<tab>)