Just check to see if the value is set, if not, use a default value instead:
$distance = (isset($_POST["distance"])) ? $_POST["distance"] : '';
$groupname = (isset($_POST["groupname"])) ? $_POST["groupname"] : '';
$name = (isset($_POST["name"])) ? $_POST["name"] : '';
$group->GroupDistance = mysql_real_escape_string($distance);
$group->GroupName = mysql_real_escape_string($groupname);
$group->Groupduration = mysql_real_escape_string($name);