As well as the complex Lie group of type E8, there are three real forms of the Lie algebra, three real forms of the group with trivial center (two of which have non-algebraic double covers, giving two further real forms), all of real dimension 248, as follows:* The compact form (which is usually the one meant if no other information is given), which is simply connected and has trivial outer automorphism group.
As well as the complex Lie group of type E8, there are three real forms of the group, all of real dimension 248, as follows:* A compact form (which is usually the one meant if no other information is given), which is simply connected and has trivial outer automorphism group.