Multiple Database Design or NOT?
I suggest:


A single database for all groups, but with
each table partitioned by group.


This should provide you with the convenience of a single database, combined with something like the performance you would expect from separate databases for each group.

Based on the comments on the related question on StackOverflow, you are using MySQL - you can find the official MySQL 5.5 Reference Manual section on partitioning here.

There is also a related StackOverflow question here, and a related blog entry here.