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The (compact real forms) Lie groups $SO(16)$ et $SU(11)$ are different, but have the same dimension ($120$).

The (compact real form) Lie group $SO(11)$, of dimension $55$, is an obvious sub-group of $SO(16)$ et $SU(11)$.

But it is the maximal (compact real form) sub-group of $SO(16)$ et $SU(11)$ ?

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