You’ll want to search your theme files for the part of the page template that is controlling those classes, likely page.php would be a good place to start.
Then once you find the part you think is controlling the output, try adding:
if( is_page(24331) ) { echo 'vertical-header'; }
For example:
<div id="page" class="layout-fullwidth <?php if( is_page(24331) ) { echo 'vertical-header'; } ?>">