In Grand unification theory, E6 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 E6/Spin(10)×SO(2). Explicitly we have that
78→450⊕16−3⊕¯163+10
27→14⊕10−2⊕161
¯27→1−4⊕102⊕¯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)