A number of wiki hosts were evaluated prior to choosing "pbwiki.com".  Priorities in this choice were ease-of-use, availability of useful features, evidence of a large user base and cost.

During setup, one of three user classes is selected: Business, Academic or Personal.  See pbwiki.com .

The Academic version appears to be the best choice for the intended purpose.  This version has a large user base (>350,000 educators) with applications ranging from grade school classrooms to college/university activity.

See the Directory of Public Educational wikis for some examples.

There is extensive help and tutorials available.  Although the language is couched in Academic termonology, it is not too much of a stretch to think of a "classroom" as a "group".

The cost is $99 per year.  Unlimited users, bandwidth and storage plus no advertisments make this wiki host a good option.