To delete a group in the Main Menu select Mesh -> Delete Groups and select one or several groups you wish to delete in the 3D viewer or in the Object Browser.
The selected groups will be listed in Delete groups with contents menu. Then click Ok button to remove the selected groups and close the menu or Apply button to remove them and proceed with the selection.
Please, note that this operation removes groups with their elements. To delete a group and leave its elements intact, right-click on the group in the Object Browser and select Delete in the pop-up menu or select the group and choose Edit -> Delete in the Main Menu.