You can see the rights of group by ls -l
in terminal to see the permissions of corresponding files.
drwxrwxr-x 3 owner group 4096 Jun 23 17:15 Calibre Library
-rw-rw-r--. 1 owner group 44444 May 25 11:36 custom 1.tar.gz
drwxr-xr-x. 4 owner group 4096 Jul 11 21:26 Desktop
drwxr-xr-x. 2 owner group 4096 Jul 9 20:35 Documents
drwxr-xr-x. 13 owner group 12288 Jul 11 12:42 Downloads
drwx------. 7 owner group 4096 Jun 23 13:21 Dropbox
Which can be further shown

You can refer to File Permissions for changing permissions. Whereas following commands are used to change it.
chmod - modify file access rights
su - temporarily become the superuser
chown - change file ownership
chgrp - change a file's group owner
EDIT : To view the files owned by the group "test" and user "luser' use FIND command
to find all the groups available on your system:
cat /etc/group |cut -d: -f1
eg. for finding the groups that the current user belongs to
groups
luser test adm cdrom sudo dip plugdev lpadmin sambashare
then looking for groups luser belongs to
groups luser
luser : test luser adm cdrom sudo dip plugdev lpadmin sambashare
Now to see the files owned by group "test" in particular path or folder. Try
find /home -group test
find /etc -group root
GUI method via Nautilus , select the Group, Permissions , Owner
options from the Nautilus Preferences menu.

Then in Nautilus File manager , by selecting Icons views you will get the group name under icon as

And in list view you will get something like
