Vertical Rule in PGF Plottable

I just learned to plot tables with pgfplottables and it feels very nice and smooth. Here is my Code example:

documentclass[14pt]{book}
usepackage{pgfplots}
usepackage{pgfplotstable}
usepackage{amsmath}
usepackage{booktabs}
begin{document}

begin{center}
pgfplotstableread{
    X          C1          C2          C3          C4
    $A$          1         1         1          1
    $B$          1         1         1          1
    $C$          1         1         1          1
    $D$          1         1         1          1
}testdata


pgfplotstabletypeset[
  every head row/.style={
    before row={toprule 
        & multicolumn{2}{c}{textbf{table}}            cmidrule{2-3}},
    after row=midrule},
  every last row/.style={after row=bottomrule},
  columns/X/.style={string type, column name={test},column type/.add={}{|}},
  columns/C1/.style={string type, column name={$a$}},
  columns/C2/.style={string type, column name={$b$}},
  columns/C3/.style={string type, column name={$c$}},
  columns/C4/.style={string type, column name={$d$}},
  columns={X, C1,C2,C3,C4},
]testdata
end{center}


end{document}

My question is about the line

columns/X/.style={string type, column name={test},column type/.add={}{|}},

It gives me a line at the right place, but the rule breaks when it reaches the horizontal line right under "X a b c d" and it doesn’t stop there but also implements a rule left to "table".

Is there a possibility to stop it right besides of $X$ without breaking when it passes the horizontal line?

Thank you!

documentclass{book}
usepackage{pgfplots}
usepackage{pgfplotstable}
usepackage{amsmath}
usepackage{booktabs}
begin{document}

begin{center}
pgfplotstableread{
    X          C1          C2          C3          C4
    $A$          1         1         1          1
    $B$          1         1         1          1
    $C$          1         1         1          1
    $D$          1         1         1          1
}testdata


pgfplotstabletypeset[
  every head row/.style={
    before row={toprule 
       multicolumn{1}{c}{} & multicolumn{2}{c}{textbf{table}}            cline{2-3}},
    after row=hline},
  every last row/.style={after row=bottomrule},
  columns/X/.style={string type, column name={test},column type/.add={}{|}},
  columns/C1/.style={string type, column name={$a$}},
  columns/C2/.style={string type, column name={$b$}},
  columns/C3/.style={string type, column name={$c$}},
  columns/C4/.style={string type, column name={$d$}},
  columns={X, C1,C2,C3,C4},
]testdata
end{center}


end{document}