BuddyPress.org

This adds the required tab –

add_action( 'groups_admin_tabs', 'add_admin_test_tab', 90, 2);
function add_admin_test_tab( $current_tab, $gslug ) {
?>
<li class="current"><a href="/admin/test">
<?php
}

edit – it works, but it’s a very bad idea not to use the API