Homotopy groups of exceptional Lie groups for Lie algebra $\mathfrak{g_2,f_4,e_6,e_7,e_8}$
It is commonly say the Lie groups of given exceptional Lie algebra $\mathfrak{g}_{2}$, ${\mathfrak {f}}_{4}$,${\mathfrak {e}}_{6}$, ${\mathfrak {e}}_{7}$, ${\mathfrak {e}}_{8}$ are $G_2$, $F_4$, $E_6$, $E_7$, $E_8$. What the homotopy groups $$\pi_d(G)$$ of these Lie groups $G$ for lower dimensions say $d=0,1,2,3,4,5$?
Partial answers are welcome!!! For example, if you know $d=1$, that can count as one answer; if you know $d=2$, that can count as another one answer.
Note that: In a previous question, I also asked whether there are more and different Lie groups of the same exceptional Lie algebra? for $\mathfrak{g_2,f_4,e_6,e_7,e_8}$. See https://en.wikipedia.org/wiki/Exceptional_Lie_algebra and Different Lie groups of the same exceptional Lie algebra? for $\mathfrak{g_2,f_4,e_6,e_7,e_8}$