A new and distinct plum tree variety, Prunus salicina, cv. ‘;Suplumfiftysix’; is characterized by having very large fruit, with reddish-black skin and red flesh. The fruit of the new variety ‘;Suplumfiftysix’; also has firm flesh, a sweet-mild flavor and a stone that is semi-free from the flesh. The date of ripening of the fruit of the new variety is approximately September 7.