Only the group owner can delete a group.
Go to the group contact card of a group that you want to delete (either by tapping on the group header name in a group shared mailbox or tapping on the group avatar in group email conversations).
Tap on the Edit button in the top right hand corner.
Use the Delete Group button at the bottom of the Edit Group page.
When you delete a group, you are permanently removing the group team site, group conversations, email messages, files, calendar events, and any other related information. If you deleted the group by mistake, you can ask your IT admin to recover the group within 30 days of it being deleted.