Using Bott periodicity, we know the stable homotopy of all classical compact lie group. So I am wondering if a similar pattern exists for exceptional Lie groups.
Unfortunately, I couldn't find a result online. Is it because it is too easy or too difficult?
A relevant paper I found is "Homotopy Groups of Compact Lie Groups E6, E7, and E8" https://projecteuclid.org/download/pdf_1/euclid.nmj/1118797372, which we don't see a period yet.