It could be that way, but maybe I'm giving you some more good info here (forgive me if you already know this thought)...
Use your primary id's and then associate the values...
So...the user table would be like...
usr_id | name | surname | groups
1 | You | Yourself | 1,2,3
And then your groups table would be something liek...
grp_id | name | description
1 | Everybody | All of the members
2 | WebDev | Team working on the website
Then you would associate where group_id=groups. You might have some people who belong to more than one group - just cozy up to your nifity explode and implode commands and you'll be good.
Good luck...v