Denote by $D_{6}$ the dihedral group of order $12$. Determine which of the following elements of $D_{6}$ belong to the conjugacy class and the centralizer of the element $a^2 b^1\in D_{6}$. Enter Y for yes and N for no.

	Conjugacy class	Centralizer
identity
$a^1$
$a^2$
$a^3$
$a^4$
$a^5$
$b$
$a b$
$a^2 b$
$a^3 b$
$a^4 b$
$a^5 b$