Try this, at least to get acquainted with the possibilities:
1. Change to the WordPress Default theme
pageofpages.php and change it to look like this:
* @package WordPress
* @subpackage Default_Theme
Template Name: PageofPages
<?php get_header(); ?>
<div id="content" class="widecolumn">
<?php wp_list_pages(); ?>
<?php get_footer(); ?>
4. Vist Pages->Add new and create a Page call it "My Page listing of Pages" and in the Template pulldown, select "PageofPages"
5. Then see how you like that by visting your blog.
6. If necessary read wp_list_pages() to decide how you might want to limit what that list of pages displays (e.g. you might decide to use custom fields to assign some value to what you call Group X pages so you would use the meta_key and meta_value parameters).