Public group chats are only available to Trillian for Business users!
Browsing and creating public group chats
Click the Trillian button in the upper left of your contact list and click Join or Start Public Group Chat:
A list of group chats you already belong to and group chats available for you to join will be presented. Double click a group chat within the group chats you can join section to join or click New to start a new public group chat: