Copy and paste the following script.
script language="ecmascript" type="text/ecmascript">
var contentTypeCollection;
var contentType;
function getContentTypeGroup() {
var clientContext = new SP.ClientContext.get_current();
if (clientContext != undefined && clientContext != null) {
var web = clientContext.get_web();
this.contentTypeCollection = web.get_contentTypes();
this.contentType = contentTypeCollection.getById("0x0100FFC434A461E47E4EB81D3FD76D42BFBF");
clientContext.load(this.contentType);
clientContext.executeQueryAsync(Function.createDelegate(this, this.onQuerySucceeded), Function.createDelegate(this, this.onQueryFailed));
}
}
function onQuerySucceeded() {
alert(this.contentType.get_group())
}
function onQueryFailed(sender, args) {
alert('Request failed. ' + args.get_message() + '\n' + args.get_stackTrace());
}</script>
<input id="btnGetContentTypeGroup" onclick="getContentTypeGroup()" type="button"
value="Get the content type group" />