One potential idea for a CS group - meet up once a week, and complete some small project together in some kind of fashion that allows for peer reviews while it's being made. So like the live coding we did in lectures, but students take part too, maybe on a rotated basis.
It'll have the upside of making something new and different each week and actually finishing it
Being able to pick up new languages and tools through watching other people use them
Helping each other learn conventions and stick to writing good, clear and sensible code
Depending on the number of people that join, it could get very heavily weighted into a large amount of people just watching what's happening and not taking part
So it could be broken down into smaller groups, like pair programming but with 3-4 people in each group as opposed to 1-2
It could also serve as a hackathon training group, as that time period would be tight
We could cover a very wide range of topics, like games, web scraping, servers, data handling and transformation, etc