Erm ... Users don't belong to Resource Groups. They belong to User Groups. Because they can belong to more than one User Group, no simple tag will display a Group for them.
Users can have a "Primary Group," but it's stored as a group ID rather than a name, so a custom snippet could display that as well.
$groupId = $modx->user->get('group');
$group = $modx->getObject('modUserGroup', $groupId);
$name = $group->get('name');
if (empty($name)) {
$name = 'No Primary Group';
}
$modx->setPlaceholder('group', $name);
$modx->setPlaceholder('group', $name);