I developed and mantain the Frontend User Manager extension that can show exactly that listing in the frontpage.
The current 0.0.6 stable release does exactly that and if you need user management in the front you can give a try to the 0.1.0alpha13 release.
Whenever you call JUserHelper::getProfile() the code in that function triggers a Joomla event 'onContentPrepareData' to which the Joomla user plugin User - Profile subscribes. This plugin adds in the profile data which has been stored for this user and returns it as an array.
However, plugins have an Access field which controls which User Groups have viewing ...
This information does exist in the frontend model, but for whatever reason, isn't actually displayed.
Copy /components/com_users/views/profile/tmpl/default_core.php to you template directory, so /templates/yourtemplate/html/com_users/profile/default_core.php and then in said template, you can dump the data object which will show all of the above, and more.
You should create a Viewing Access Level called 'Fred' or 'Training Only' and include only the Group 'Training' in this Viewing Access Level.
In your Menu you change your Access Level from 'Registered' to 'Training Only' or 'Fred' or whatever you called it.
It gets confusing with Group and Viewing Access Levels because as shipped they both share the stock ...