This is a powershell script that can query sharepoint to get the Account and Name values for a group given the domain\username format of the user.

test-sharepoint-group-query.ps1

$sharepointSite = "http://102.15.12.153"
$loginUserName = "some-username"
$domain = "THEDOMAIN" # must be upper case
$groupNameToQueryFor = "GROUPNAME-TO-QUERY-FOR" # must be upper case

$passwordSecure = Read-Host "What is $loginUserName's password?" -AsSecureString
$credential = New-Object –TypeName "System.Management.Automation.PSCredential" –ArgumentList $loginUserName, $passwordSecure
$base64AuthInfo = [Convert]::ToBase64String([Text.Encoding]::ASCII.GetBytes(("{0}:{1}" -f $loginUserName,$passwordSecure)))
$response = Invoke-RestMethod -Method Get -Uri "$sharepointSite/_vti_bin/listdata.svc/UserInformationList?`$filter=substringof(%27$domain%5C$groupNameToQueryFor%27%2Ctoupper(Name))%20eq%20true%20and%20ContentType%20eq%20%27DomainGroup%27" -Headers @{Authorization = "Basic $base64AuthInfo" } -Credential $credential -ContentType "text/xml"
$ns = @{d="http://schemas.microsoft.com/ado/2007/08/dataservices"}
$Account = Select-Xml -Xml $response -XPath '//d:Account' -Namespace $ns
$Account | Foreach {$_.Node}
$Name = Select-Xml -Xml $response -XPath '//d:Name' -Namespace $ns
$Name | Foreach {$_.Node}