Fatto generale: 564 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Fatto matematico: 564 is the number of 13-ominoes with a horizontal or vertical line of symmetry.
Trivia: 564 is a boring number.
Data storica: July 17th is the day in 1402 that Zhu Di, better known by his era name as the Yongle Emperor, assumes the throne over the Ming Dynasty of China.