get magento customer group id and magento group name from admin side

You need to load the customer model by the customer id, e.g.:

$customer = Mage::getModel('customer/customer')->load($customerId);

Then based on the customer model you can get the group id with $customer->getGroupId()

Mage::helper('customer')->getGroups() returns a list of groups excluding non-logged in one, based on it you can determine customer_group_code which will be the customer assigned group name