Identifying which known groups are the most similar or most dissimilar
You only have five groups, so full blown clustering is probably not a good idea here, but looking at similarity scores between the group vectors may be insightful. An easy one to try at first would be cosine similarity, which essentially measures the angle between each of your group vectors:

similarity = $cos(\theta)$ = $\frac{\mathbf{A} \cdot \mathbf{B}}{||\mathbf{A}||_2 ||\mathbf{B}||_2}$

where $\mathbf{A} \cdot \mathbf{B}$ gives the dot product of two vectors, and $||\mathbf{A}||_2$ is the magnitude of a vector $\mathbf{A}$.

All of your vector values are positive, so the result will be in the range $(0, 1)$. The closer this value is to $1$, the more similar the vectors. $0$ means they are completely decorrelated (vectors are orthogonal). You can compare the cosine similarities of each pair of groups to work out which ones are most similar/dissimilar.