What is the primary function of the z gene in the lac operon?

The lac operon consists of one regulatory gene (the i gene, inhibitor) and three structural genes (z, y, and a). 

The i gene codes for the repressor of the lac operon.

 The z gene codes for beta-galactosidase (β-gal), which is primarily responsible for the hydrolysis of the disaccharide, lactose into its monomeric units, galactose and glucose.

 The y gene codes for permease, which increases permeability of the cell to β-galactosides. 

The a gene encodes a transacetylase.