Use Google Calendar with Google Groups

https://support.google.com/groups/answer/60652?hl=en

Using google calendar with google groups will make your communication with group members easier and efficient.

Here is some tips how to use google calendar for group use:

1- Click on calendar on when you are on your google account. Click on arrow on your 'My Calendar',
then click on Create an event on this calendar.

2.  Then fill up title, date and time, location, description, event color, reminders, and privacy. (leave privacy on default)

3. Add guests: add email address who you want to invite for the event.

4. Click on SAVE, and you are done.

This way everyone on the group can add events on this calendar and these notifications will show on your google group's calendar.  .