SYMMETRIC GROUP S4 and S5

SYMMETRIC GROUP S_{4 and} S5
S_4
= {I,(12),(13),(14),(23),(24),(34),
         (12)(34),(13)(24),(14)(23), 
         (123),(124),(132),(134),(142),(143),(234),(243),
        (1234),(1243),(1324),(1342),(1423),(1432)} 
S5
={I,(12),(13),(14),(15),(23),(24),(25),(34),(35),(45),(12)(34),(12)(35),(12)(45),(13)(24),(13)(25),(13)(45),(14)(23),(14)(25),(14)(35),(15)(23),(15)(24),(15)(34),(23)(45),(24)(35),(25)(34),(123),(124),(125),(132),(134),(135),(142),(143),(145), (152),(153),(154),(234),(235),(243),(245),(253),(254),(345),(354),(12)(345),(12)(354),(13)(245),(13)(254),(14)(235),(14)(253),(15)(234), (15)(243),(23)(145),(23)(154),(24)(135),(24)(153),(25)(134),(25)(143), (34)(125),(34)(152),(35)(124),(35)(142),(45) (123),(45)(132),(1234),(1235),(1245),(1324),(1325),(1345),(1423),(1425),(1435),(1523), (1524),(1534),(2345),(2435),(2534),(1243),(1253),(1254),(1342),(1352), (1354),(1432),(1452),(1453),(1532),(1542),(1543),(2354),(2453),(2543),(12345),(12354),(12453),(13245),(13254),(13452),(14235),(14253),(14352), (15234),(15243),(15342),(12435),(12534),(12543),(13425),(13524),(13542), (14325)(14523),(14532),(15324),(15423),(15432)}