Re-arranging columns on JTables

I’m only new to Java UI work, and was surprised to see how easy it is to work with tables.
In my case I’m trying to build an application where the user need to be able to sort columns manually.
A few things I’ve learnt:
JTables only show column headers if the table is placed inside a JScrollPane
It’s really annoying to drag-and-drop narrow, resizable columns, so turn off resizing. I ended up with this user-rearrangeable table:
Basic code for this, thanks to Google Windowbuilder:
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import java.awt.EventQueue;

import javax.swing.JFrame;
import javax.swing.JTable;
import javax.swing.table.DefaultTableModel;
import javax.swing.JScrollPane;

public class TableTestWindow {
    private JFrame frame;
    private JTable table;

    /**
     * Launch the application.
     */
    public static void main(String[] args) {
        EventQueue.invokeLater(new Runnable() {
            public void run() {
                try {
                    TableTestWindow window = new TableTestWindow();
                    window.frame.setVisible(true);
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
        });
    }

    /**
     * Create the application.
     */
    public TableTestWindow() {
        initialize();
    }

    /**
     * Initialize the contents of the frame.
     */
    private void initialize() {
        frame = new JFrame();
        frame.setBounds(100, 100, 525, 520);
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.getContentPane().setLayout(null);

        JScrollPane scrollPane = new JScrollPane();
        scrollPane.setBounds(12, 12, 460, 440);
        frame.getContentPane().add(scrollPane);

        table = new JTable();
        table.setFillsViewportHeight(true);
        scrollPane.setViewportView(table);
        table.setRowSelectionAllowed(false);
        table.setColumnSelectionAllowed(true);
        table.setModel(new DefaultTableModel(
            new Object[][] {
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
                {null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null},
            },
            new String[] {
                "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z"
            }
        ) {
            /**
             * Java coughs up warnings if we dont do this
             */
            private static final long serialVersionUID = 1L;

            public Class getColumnClass(int columnIndex) {
                return String.class;
            }

            public boolean isCellEditable(int row, int column) {
                return false;
            }
        });

        for(int i = 0; i < 26; i++) {
            table.getColumnModel().getColumn(i).setResizable(false);
            table.getColumnModel().getColumn(i).setPreferredWidth(20);
        }

    }
}