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there exist tables with group theory breaking patters and branching rules such as

[tex]E_7 \rightarrow E_6 \times U(1)[/tex]

[tex]133 \rightarrow 78 + 1 + 27 + \bar{27}[/tex]

[tex]56 \rightarrow 1 + 1 + 27 + \bar{27}[/tex]

What is missing is the U(1) charge. Does anyone know how to obtain it?

Perhaps it could be done by using a character formula but then I would need the characters of these representations.

Any help would be appreciated.