JMSXGroupId has no effect on JMSProducer

Scenario

I'm setting the JMSXGroupID on a JMSProducer to achieve message delivery in the correct order. The consumer is a message-driven bean.

        JMSProducer producer = context.createProducer();
        producer = producer.setProperty("JMSXGroupID", "sequential");
        producer = producer.setProperty("foo", "bar");
        for (int i = 0; i < 50; i++) {
            msgNumber++;
            String text = "This is message " + msgNumber;
            producer.send(queue, text);
        }

Expected Behaviour

The messages are received in the correct order, the properties JMSXGroupID and foo are set on the receiver side.

Actual Behaviour

The messages are received in random order. Property foo is set, but property JMSXGroupID is null on the receiver side.

Workaround

Create a TextMessage and set the properties on the message, not on the producer.