You are correct that the Group has a private constructor, and you cannot use it.
Looking at the source code the method called
public static PaginatedResult<User> getMembers(String group, int page, String apiKey)
in de.umass.lastfm.Group lets you get all users, and it is static, so you can access it without creating a Group object first.
Do something like
PaginatedResult<de.umass.lastfm.User> users = Group.getMembers("Belgium", key);