Adding a unique class when using a grouping field

Would it be possible to add a unique class to the <h3> and the <div> below it?

This could come in handy when the headers need a different background colour or image (as in my case now).

I know the use of unique id's is a bit delicate, but could a unique class cause any trouble?

Here's what I'm looking for (see "group_1"):

<div class="ui-accordion" role="tablist">
    <h3 class="views-accordion-brands-block-header group_1" role="tab" aria-expanded="true" aria-selected="true" tabindex="0">
       <span class="ui-icon ui-icon-triangle-1-s"></span>
       <a href="#brands-block-0" tabindex="-1"> Stanley </a>
    </h3>
    <div class="ui-accordion-content ui-helper-reset ui-widget-content ui-corner-bottom ui-accordion-content-active group_1" style="height: 485.4px;" role="tabpanel">
       (view rows)
     </div>
</div>

A class with a number would be enough really, such as "group_1" for instance.