  A complete realistic model based on the supersymmetric version of $E_6$ is
presented. It consists of three copies of matter 27, and a Higgs sector made of
$2\times(27+\bar{27})+351'+\bar{351'}$ representations. An analytic solution to
the equations of motion is found which spontaneously breaks the gauge group
into the Standard Model. The light fermion mass matrices are written down
explicitly as non-linear functions of three Yukawa matrices. This contribution
is based on Ref. [1].
