Assessing Group Similarities and Dissimilarities Post PCA The goal is to assess similarity and dissimilarity between 6 known groups. 

The original data began with the 6 known groups and 2,700+ variables all on a scale of 0 to 100.

I have performed PCA to reduce the 2700+ variables into 5 principal components using the dudi.pca function from the ade4 package in R. Here are the Eigenvalues for the components:

      eigenvalue variance.percent cumulative.variance.percent
Dim.1   998.3274        36.635867                    36.63587
Dim.2   670.1278        24.591848                    61.22771
Dim.3   482.2372        17.696776                    78.92449
Dim.4   352.2806        12.927728                    91.85222
Dim.5   222.0270         8.147781                   100.00000


I would now like to assess the distances between the 6 known groups. Is this done as simply as generating a distance matrix using each group's coordinates for each of the principal components? If so, I am leaning towards using Manhattan distance to get the absolute distance.

Here are the coordinates of each group:

           Dim.1       Dim.2       Dim.3        Dim.4        Dim.5
Group 1    69.019038    7.940190    0.4985599  - 6.847178     0.3964117
Group 2   -16.302322  -25.965373  -29.3084201  -23.013430     9.9183010
Group 3   -26.313850   50.159662    6.9486408  -10.713924     5.2883152
Group 4   -12.800767  -26.211432   39.5067264  - 8.775551   - 8.8840592
Group 5   - 9.228404    2.648632  -20.4297314   16.685426   -26.8559444
Group 6   - 4.373694   -8.571679    2.7842244   32.664657    20.1369757


If not, what would be the appropriate way to assess individual similarity/ dissimilarity post PCA?
What does the distance between groups mean for your problem? Answering that problem would help you pick a distance metric.  

Assuming you pick e.g. Euclidean distance, one simple way to find inter-group distance would be to first calculate the group centroid, i.e. average location of each group by averaging the locations of each group together.  You can do this by just averaging all the 5x1 vectors belonging to a group, and repeat for each group.  Then calculate the Euclidean distance between the resulting 6 centroids, giving you a 6x6 distance matrix.