How can I check the permissions of a specific group?

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

Groups don't have permissions so to say...

Each file/folder is owned by a user and a group. If your group owns the file/folder then you'll have the permissions in the second group of permissions.

For example, let's say a file has:

-rwxrw-r--

Split this into thirds, excluding the first character (this is a special character):

• rwx (Owner) - The owner has read/write and execute permissions.

• rw- (Group) - The group has read and write permissions.

• r-- (Everyone else) - Everyone else has read permissions.

You can change these permissions using chmod and you can change who owns them by using chown. To learn more about these commands, open a terminal and type man chmod or man chown.

Try:

find / -group name_of_group