Powershell commands are very powerful and its mainly used for sharepoint admistratve tasks. Below are the powershell commands to change the ownership of a SharePoint Group.
#Get the SPWeb Object
$web = Get-SPWeb http://mysites
#Find the Group
$group = $web.SiteGroups["CustomGroup"]
#Ensure that user is a part of authenticated users
$user = $web.EnsureUser("domain\username")
#Assign that user as the owner
$group.Owner = $user
#Update the Group
Happy SharePointing :-)