This might sound easy with /etc/group and /etc/passwd, but what if you use libnss-mysql for example and need to try if it works?

So just forget grepping config files. Here are the real commands:

Members of a group:

getent group GROUPNAME

Replace GROUPNAME with the group you want to check.

Groups of a user:

groups USERNAME

Replace USERNAME with the name of the user to check.

Checked on Debian, not sure if it works on any Linux/Unix.