#Get the SPWeb
$web = Get-SPWeb "URL"

#Get the Group
$group = $web.SiteGroups["Group 1"]
$group = $web.SiteGroups["Group 2"]
#Get the User
$user = $web.EnsureUser("domainuser")

#Assign that user as the owner
$group.Owner = $user

#Update the Group
$group.Update()