IDG Answers is a community of experts who are passionate about technology. Ask a question or answer one below.
I asked a friend of mine who works at the local university. He said they use Sakai (LINK) for class scheduling and student communication, but he wasn’t sure about Google Calendar integration. Also, it runs on servers, I’m not sure if there is a cloud version. For small groups have you considered just setting up a Google+ Circle for each class, you can then do group notifications that will send out reminders of the schedule ahead of time. Obviously those are opposite ends of the possible solutions spectrum.
I don’t know of a specific solution off the top of my head. However, I have a friend who works in IT at a local university. Next time I see him, I will ask him about this and see what they use. It may be a little while before I speak with him and I can’t promise he will be able to help, but I will post an update if he can provide any suggests.