If you are the owner of the group, you can change most things about the group. If you are not the group owner, you will need to have the group password to modify any group settings.
To change ownership, go to https://account.my.cae.wisc.edu/group and log in using your CAE information.
Under the Groups section you will see the group you want to modify.
Click on the group name to select it and go to the group's info page.
Click on the Edit group link.
Put the new owner's CAE login name in the Owner box. Note that the owner must also be a member of the group or this will not work. If the new owner is not currently a member, add the owner, then click the Update button before changing the owner. Instructions on adding members can be found here.
Click the Update button.
That's all you need to do. It will take a little while for the change to get to all our servers.