It sort of depends on where that is being added. Is that a custom header? Or are you trying to add them on the same line as the logo?
If on the same line as the logo, this is close (create it as a custom component and enable it as part of your theme, in the </head> section)
<script type="text/discourse-plugin" version="0.2">
api.decorateWidget('home-logo:after', helper => {
const user = Discourse.User.current();
if(user.primary_group_name.toLowerCase() === "group1") {
return helper.h('div#top-navbar.container', [
helper.h('span#top-navbar-links', [
helper.h('a.btn.btn-lg.btn-primary', {
href:'https://www.demo.com/',
text:'<i class="fa fa-flag fa-2x pull-left"></i> Click here<br>for demo!' // not sure if this will work
})
])
]);
}
});
</script>