There isn't a fixed maximum number of contacts per group in your account - you should be able to get many more than 3,000 in there without issues.
Please let me know a bit about the process you're taking, and what sort of errors or specific roadblocks you're running into? Are you attempting to import a large list? If so, is the import process going forward, and you're getting a failure message? Or, is the import not even running through the entire process?
Any additional details you might be able to provide about what specifically you're experience would be great. Thanks so much!