It's not possible to give a group a specific color as of now. However, we do understand the value of project colors to easily differentiate between groups and projects in the calendar - and it is part of our roadmap.
Alternative to project colors
Until this feature is released, you can alternative toggle groups on/off. In the blue side you'll see a checkbox next to each group. Tick the box to hide/display the group's todos and meetings from the calendar.