Widget won't appear on my site

<?php
/*
 * Plugin Name: GitHub Statistics Plugin
 * Plugin URI: http://ajdoo.se/wpgithub-statistics-wordpress-plugin
 * Description: Helps you to display statistics from GitHub
 * Version: 1.0
 * Author: Caroline Forslund
 * Author URI: http://www.carolineforslund.se
 * Licence: GPL2
*/

/*
 * Add a link to the plugin admin menu
 * under 'Settings > GitHub Statistics'
*/

function wpgithub_statistics_menu(){

    /* Use the add_options_page_function
     * add_options_page( $page_title, $menu_title, $capability, $menu-slug, $function 
    */
    add_options_page(
        'GitHub Statistics Plugin',
        'GitHub Statistics',
        'manage_options',
        'wpgithub-statistics',
        'wpgithub_statistics_options_page'
    );
}
add_action( 'admin_menu', 'wpgithub_statistics_menu' );

function wpgithub_statistics_options_page() {
    if( !current_user_can( 'manage_options' ) ) {
        wp_die( 'You do not have sufficient permission to access this page.' );
    }
    echo '<p>Welcome to GitHub Statistics plugin page!</p>';
}
 // WIDGET -------------------------------------------------------------

class Wpgithub_Statistics_Widget extends WP_Widget {

    function wpgithub_statistics_widget() {
        // Instantiate the parent object
        parent::__construct( false, 'GitHub Statistics Widget' );
    }

    function widget( $args, $instance ) {
        // Widget output
        extract( $args );
        $title = apply_filter( 'widget_title', $instance['title'] ); //Let the user choose title of the Widget
        require( 'inc/front-end.php' );
    }
    function update( $new_instance, $old_instance ) {
        // Save widget options
        $instance = $old_instance;
        $instance['title'] = strip_tags( $new_instance['title'] ); //strip_tags function prevent HTML from displaying up in the form
        return $instance; //the new instance replace the old instance
    }

    function form( $instance ) {
        // Output admin widget options form
        $title = esc_attr( $instance['title'] ); //Poll in the instance and allow us to get the entered title
        require( 'inc/widget-fields.php' );
    }
}
function wpgithub_statistics_register_widget s() {
    register_widget( 'Wpgithub_Statistics_Widget' );
}
add_action( 'widgets_init', 'wpgithub_statistics_register_widgets' );
?>

<p>
    <label>Title</label>
    <input class="widefat" name="<?php echo $this->get_field_name('title'); ?>" type="text" value="<?php echo $title; ?>" />
</p>

<?php
    echo $before_widget;
    echo $before_title . $title . $after_title;
    echo '<p>What I want to show in the Widget</p>';
    echo $after_widget;
?>