When you share a folder or file on Google Drive it will give people or a group a role that enables permissions.
Role Definitions
Manager - manages the people, content and settings
Content Manager - add, edit, delete and share content
Contributor - add, edit, and share files
Commenter - can comment on files with comment options
Viewer - can see files, but cannot edit them
To see your groups, login to Google and to groups.google.com. You will see a list of groups where you can read group messages.
To send an email to everyone in a group, the above groups.google.com will show an email address for the group.
To find more about Google Groups, go to https://support.google.com/groups
Role Definitions
Group member - gets email from the group and can login to the group to see messages
Group managers - can add and remove members, can moderate discussions, can approve posts if they need to be approved
Group owners - can do all the above and can delete the group
If you are a group leader here's some help for you.
How to add people to your group
Invite people to join your Google group, or add members directly.
Share Google Docs and Calendars directly with your group
Working with shared documents and calendars has never been easier than with Google Groups. Share your files with the group and it will automatically update whenever someone is added or removed from the group.
Learn about sharing with Groups
Get organized
Google Groups has several options for organizing content in your discussion group including: categories, tags, and tracking topic resolutions.