Use the -SearchBase and maybe the -SearchScope parameters on the Get-ADGroup to target your search.
The "associated properties" can be extensive and probably not all (or even many) of them would be useful to you. Also, getting the membership of a group into a CSV isn't as simple as adding the member property to the CSV.
You'll find lots of examples of how to do what you're asking if you search the web. Maybe not all of them will do exactly what you want, but you should be able to use them as a basis for you own script.
If you need help with your script, post the code you're using along with a clear explanation of your goal and the particular problem you're having (including any exception messages).