Add column to Admin Table show the feature image of a post.

functions.php

<?php
/*
 * Adds the new column to the Admin Post View as the first column.
 */
function my_columns_filter( $columns ) {
	$column_thumbnail = array( 'thumbnail' => 'Thumbnail' );
	$columns          = array_slice( $columns, 0, 1, true ) + $column_thumbnail + array_slice( $columns, 1, null, true );
	
	return $columns;
}
add_filter( 'manage_edit-post_columns', 'my_columns_filter' );

function my_column_action( $column ) {
	if ( $column === 'thumbnail' && has_post_thumbnail() ) {
		the_post_thumbnail( array( 80, 80 ) );
	}
}

add_action( 'manage_posts_custom_column', 'my_column_action' );

/*
 * Sets the width of the Thumbnail column.
 */
function wp98_column_width() {
	$screen = get_current_screen();
	
	if ( isset( $screen ) && $screen->id == 'edit-post' ) {
		echo '<style type="text/css">';
		echo '.column-thumbnail { width:80px !important; overflow:hidden }';
      	echo '.column-thumbnail img { width:80px !important; }';
		echo '</style>';
	}
}
add_action( 'admin_head', 'wp98_column_width' );