Let $G$ be a **semisimple Lie group**. Denote $d(G)$ as the maximal integer $p$ such
that $\mathbb{Z}^p$ is isomorphic to a discrete subgroup of $G$ and $c(G)$ is the maximal integer $q$ such that $\mathbb{R}^q$ is isomorphic to a closed subgroup of $G$.

is there a way to compute $d(G)$ and $c(G)$?

if you have any related references, please share them whit me.