We study a universal property of $Sp(2)$ in the category of $3$-local homotopy associative, homotopy commutative $H$-spaces. We show that while $Sp(2)$ fails to be universal in the full category, there is a subcategory in which it is universal for its $7$-skeleton.
"A universal property for $Sp(2)$ at the prime $3$." Homology Homotopy Appl. 11 (1) 1 - 15, 2009.