Cycle notation

A concise to describe a specific permutation.

A permutation group can then be described in terms of the generating set of a group of specific elements given in cycle notation.

E.g. en.wikipedia.org/w/index.php?title=Mathieu_group&oldid=1034060469#Permutation_groups mentions that the Mathieu group $M_{1}1$ is generated by three elements:which feels quite compact for a simple group with 95040 elements, doesn't it!