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$E_{6(n)}$ means that $n$ is the dimension of the group $E_6$ minus twice the dimension of a maximal compact subgroup.
example: $E_{6(6)}$ of dimension 78 has maximal compact subgroup ${\rm Sp}(4)/\mathbb{Z}_2$ of dimension 36.
$E_{6(n)}$ means that $n$ is the dimension of the group minus twice the dimension of a maximal compact subgroup.
