I am trying to find the number of conjugacy classes of the Lie group $Sp(6,\mathbb{R})$, and identify which elements each of them contains (in matrix form).
When searching literature on the topic, I find lots of examples where the conjugacy classes are calculated for discrete groups but I can't seem to find something similar for Lie groups. I understand that because it is not discrete there are an infinite number of possible transformation matrices, but we shouldn't we be able to define a general form those matrices should have? E.g. a matrix with all zero values in the bottom left $3\times3$ matrix is not conjugate to a matrix with all zero values in the bottom right $3\times3$ matrix.