# General linear group analogs

The Wikipedia pages for $$E_6$$ and $$E_7$$ list three series of groups notated as each of $$E_6(q)$$, $$^2E_6(q)$$, and $$E_7(q)$$:

• The simple form, analogous to $$\operatorname{PSL}_n(q)$$
• The adjoint form, analogous to $$\operatorname{PGL}_n(q)$$
• The universal form, analogous to $$\operatorname{SL}_n(q)$$

Is there a fourth series analogous to $$\operatorname{GL}_n(q)$$?

• But the general linear group is not semisimple, so it is not like the others. Oct 3 at 16:51
• Yet it still has analogs for the classical group families in the form of the general unitary groups, general symplectic groups, and pin groups. Oct 3 at 17:49