In Grand unification theory, $E_6$ appears as a possible gauge group which, after a suitable symmetry breaking, gives rise to the gauge group of the standard model $$SU(3) × SU(2) × U(1)$$

This is achieving via the breaking to $Spin(10) × SO(2)$ and then to $SO(10) × U(1)$ . According with this, the physical states will appear in representations of the coset-space $E_6 / Spin(10)×SO(2)$. Explicitly we have that

$$78 \rightarrow 45_0 \oplus 16_{-3} \oplus \overline{16}_3 + 1_0 $$

$$27 \rightarrow 1_4 \oplus 10_{-2} \oplus 16_1$$

$$\bar{27} \rightarrow 1_{-4} \oplus 10_2 \oplus \overline{16}_{-1}$$

Where the subscript denotes the $SO(2)$ charge. In such way, we can get the Standard Model's elementary fermions and Higgs boson.

Reference (Adaptation from)

http://en.wikipedia.org/wiki/E6_(mathematics)