One question to test the permission

I know test commands give us:
test -w filename - to test if file exists and writeable
test -x filename - to test if file exists and executable
test -r filename - to test if file exists and readable

How do I test if the permission is writeable or readable or executable by group users and everybody? As far as I know -w -x -r is to test for owners, am I right?

No, it tests whether the current user has that right. Which may be through owning the file, or by being in the right group for somebody elses file, or by the file have the appropriate world rights.