Topped only by Allium Allium altissimum 'Goliath', A. giganteum is the second tallest Allium available. Native to central Europe and Asia, it will really only reach its full 150cm (5'), if you plant it in deep, fertile, well-drained, sunny soil. 

Flower heads, or inflorescences, are 5" (12.5cm) wide, and densely packed with small (.5"; 1.25cm wide) deep violet flowers which have a faint blue hue. Leaves are pale green. They begin to die back when flowers emerge. 

A. giganteium has been awarded the Royal Horticulture Society's Award of Garden Merit, but it you want something even bigger and better, try Allium giganteum 'Ambassador', an improved version with 20 cm (8") flowers. 

Propagate by seed or by detaching small bulbils from the main bulb - Allium giganteum naturalizes readily.