Simple BorderLayout problem

Hello, I have a problem with BorderLayout, and I bet it's really simple.
I have JPanel with a TitledBorder (like a "group" widget) and this
JPanel contains a button.

Now I want to displays this JPanel centered horizontally and vertically
and I don't want it to occupy all the space of the client area of the
JFrame.

I tried this:
package main;

import java.awt.BorderLayout;

import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.border.TitledBorder;

public class CenteredGroup {

   CenteredGroup() {
     frame.setSize(1024, 768);
     frame.setLocationRelativeTo(null);
     frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

     JPanel contentPane = (JPanel)frame.getContentPane();

     BorderLayout borderLayout = new BorderLayout(50, 50);

     frame.setLayout(borderLayout);

     contentPane.setLayout(borderLayout);

     JPanel groupPanel = new JPanel();

     groupPanel.setBorder(new TitledBorder("This is my group text."));

     JButton button = new JButton("A button");

     groupPanel.add(button);

     contentPane.add(groupPanel, BorderLayout.CENTER);

     frame.setVisible(true);
   }

   public static void main(String[] args) {
     new CenteredGroup();
   }

   JFrame frame = new JFrame("Centered Group");
}

However, the "group control" occupies the entire client area of the
frame. Why?

I can provide a screenshot of what it looks like and how I want it to
look like if you have trouble understanding my problem description.

- F