Magento: Get customer group Id and group name

<?php
    // Check if customer is logged in
    $login = Mage::getSingleton('customer/session')->isLoggedIn(); //Check if User is Logged In
    if($login)
    {
        $groupId = Mage::getSingleton('customer/session')->getCustomerGroupId(); //Get Customers Group ID

        echo "Group ID ::  ".$groupId;

        $group = Mage::getModel('customer/group')->load($groupId);
        
        echo "Group Name :: ".$group->getCode();

    }
   ?>