Mediaeval Florentine family (6)
I believe the answer is:
medici
(Other definitions for medici that I've seen before include "Famous Florentine family name" , "Name of powerful Florentine family in 15th-17th centuries" , "Name of powerful Italian family in 15th-17th centuries" , "Italian family who ruled Florence in the 15th century" , "Noted Florentine family" .)