Groups themselves don't give any permissions, it only puts users into a particular category. Permissions are set on files which you can see using:
ls -l
$ ls -l su*
-r-sr-xr-x 1 root wheel 14500 Jul 18 22:24 su*
-r-xr-xr-x 2 root wheel 8860 Jul 18 22:24 sum*
$
From the above code...