Important properties of alternating groupA 6

By using electric computer machine, via computation method, we obtained some important properties of alternating groupA ₆, as below: 1)A ₆ has 501 subgroups in total, and for each subgroup we give its generators; 2) the index ofA ₆’s subgroup can only be 1,2,3,4,5,6,8,9,10,12,18,24,36,60,360; 3) all subgroups ofA ₆ are separated into 22 conjugate classes, and the subgroups contained in each class are listed. Foundation item: Supported by the Natural Science Foundation of Hubei Province (99J165) Biography: HUANG Ben-wen(1948-), male, Associate professor, research interest is in computation group.