@Jürgen Kanz, please take a look at the guide on proper post format: http://wolfr.am/READ-1ST
You can find out about the internal NN used by simply running (in your case):
First[nn]
and then you can dig deeper with things like:
nn[[1, "Model"]]
nn[[1, "Model", "Network"]]
where you find, among many others, things like:
Keep in mind that the net is applied to the preprocessed data, not the data itself. To reduce preprocessing, you can use
nn = Classify[ trainSet , FeatureExtractor -> "Minimal", Method ->...]
You can also probably just design your own net: