You will need the Full Write Groups permission to edit a group.
Open the Group
Click Groups in the left-hand menu to open the Listing. Find the group you want to edit and either click the group name or click the 3-dots menu at the start of the row and choose View.
Edit the Group
From the group's detail page, click the Actions button in the upper-right and select Edit group.
A pop-up will appear where you can update the group's details. See How do I add a group? for an explanation of the available fields.