How do I switch focus groups (via keyboard) immediately?

When traversing from one focus group to the next (with tab on keyboard) I expect the focus to move to the first field in the next group, but it seems to focus on nothing - and then another tab moves into that group.

class MyHomePage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Center(
        child: SizedBox(
          width: double.infinity,
          child: Row(
            mainAxisAlignment: MainAxisAlignment.spaceEvenly,
            children: [
              for (var i = 0; i < 2; i++)
                FocusableActionDetector(
                  onFocusChange: (focused) {
                    if (!focused) {
                      print('Have left focus group');
                    }
                  },
                  child: Column(
                    mainAxisAlignment: MainAxisAlignment.center,
                    children: [
                      for (var i = 0; i < 3; i++)
                        SizedBox(
                          width: 150,
                          child: TextField(),
                        ),
                    ],
                  ),
                ),
            ],
          ),
        ),
      ),
    );
  }
}

Dartpad example

I expect that after the last field in the first group a press of Tab should move focus immediately to the first item in the next focus group.

I have tried all manner of FocusNode, FocusScope, FocusScope.of(context).___, however I am finding the focus management in Flutter a bit confusing.