From the computation of some lower dimension $N$ of $Sp(N)$ group,
we see that the homotopy groups are:
at least for $N=1,2,3,4,5.$
Question: Are these results generally true for any $N$? If so, are there some simple explanations and intuitions behind?
One attempt may be using the Bott periodicity theorem.
What else topological properties of $Sp(N)$ to gain us some better intuitions/explanations?
p.s. My notations may be different from Stable homotopy groups of $Sp(2n)$, the above $Sp(N)$ means $Sp(2n)$ there.