GroupGenerators

GroupGenerators[group] returns a list of generators of group.

Examples

Get generators of the symmetric group:

GroupGenerators[SymmetricGroup[4]]
(* {Cycles[{{1, 2}}], Cycles[{{1, 2, 3, 4}}]} *)

Get generators of the alternating group:

GroupGenerators[AlternatingGroup[5]]

Please visit the official Wolfram Language Reference for more details.