I am not quite sure what you mean by "host an online study group".
If it is about people collaborate to learn something, I think moodle is what you are looking for.
Here is the wikipedia lemma for moodle:
Moodle is a free and open source
e-learning software platform, also
known as a Course Management System,
Learning Management System, or Virtual
Learning Environment. It has a
significant user base with 49,256
registered sites with 28,177,443 users
in 2,571,855 courses (as of February,
2009).
Here is how the moodle people describe it themselves:
Moodle is an Open Source Course
Management System (CMS), also known as
a Learning Management System (LMS) or
a Virtual Learning Environment (VLE).
It has become very popular among
educators around the world as a tool
for creating online dynamic web sites
for their students.
It is not written in Python or C#, but PHP and released under GPL.
You can install it on your webserver or use free moodle hosting like e-socrates.