An application can perform poorly for at least two reasons -
the hardware and software environment is not suited to the application. Possible, as shared hosting does provide the strongest environment, memory is limited and everything is shared. An application that requires more resource will be constrained.
The application can be written in a way that it simply cannot function well in a limited environment or that it just performs poorly in general.
I can tell you that I have no experience with egroupware - although I have considered installing it myself. I wasn't trying to imply your choice was bad. I really don't have a list of actual alternatives available.
I was just trying to let you know that many applications do take a little bit for the server to adjust to the first time it's started. JSP based systems are REALLY bad about that. (not to imply that egroupware is JSP based, I know it isn't because it wouldn't run here if it was).
The wiki doesn't have any hints on egroupware. Maybe someone else here has experience with it.
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