+2\,M_{d_{1}d_{3}}\,M_{d_{2}d_{3}}\,M_{d_{2}d_{4}}\,
      M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,M_{d_{4}d_{7}}\nl
      \off{3827636}
      +M_{d_{1}d_{3}}\,M_{d_{2}d_{3}}\,M_{d_{2}d_{6}}\,
      M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,M_{d_{6}d_{7}}
      -2\,M_{d_{1}d_{3}}\nl
      \off{3827636}
      \,M_{d_{2}d_{3}}\,M_{d_{2}d_{7}}\,M_{d_{4}d_{5}}\,
      M_{d_{4}d_{6}}\,M_{d_{4}d_{7}}
      +2\,M_{d_{1}d_{3}}\,M_{d_{2}d_{3}}\nl
      \off{3827636}
      \,M_{d_{2}d_{7}}\,M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,
      M_{d_{6}d_{7}}
      -2\,M_{d_{1}d_{3}}\,M_{d_{2}d_{3}}\,M_{d_{3}d_{4}}\,
      \nl
      \off{3827636}
      M_{d_{3}d_{5}}\,M_{d_{3}d_{6}}\,M_{d_{3}d_{7}}
      +12\,M_{d_{1}d_{3}}\,M_{d_{2}d_{3}}\,
      M_{d_{3}d_{4}}\,M_{d_{3}d_{6}}\nl
      \off{3827636}
      \,M_{d_{3}d_{7}}\,M_{d_{4}d_{5}}
      -6\,M_{d_{1}d_{3}}\,M_{d_{2}d_{3}}\,M_{d_{3}d_{4}}\,
      M_{d_{3}d_{6}}\,M_{d_{4}d_{5}}\nl
      \off{3827636}
      \,M_{d_{6}d_{7}}
      -5\,M_{d_{1}d_{3}}\,M_{d_{2}d_{3}}\,M_{d_{3}d_{4}}\,
      M_{d_{3}d_{7}}\,M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\nl
      \off{3827636}
      +5\,M_{d_{1}d_{3}}\,M_{d_{2}d_{3}}\,M_{d_{3}d_{4}}\,
      M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,M_{d_{4}d_{7}}\nl
      \off{3827636}
      +5\,M_{d_{1}d_{3}}\,M_{d_{2}d_{3}}\,M_{d_{3}d_{6}}\,
      M_{d_{3}d_{7}}\,M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\nl
      \off{3827636}
      +13\,M_{d_{1}d_{3}}\,M_{d_{2}d_{3}}\,
      M_{d_{3}d_{6}}\,M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,
      M_{d_{6}d_{7}}\nl
      \off{3827636}
      -5\,M_{d_{1}d_{3}}\,M_{d_{2}d_{3}}\,M_{d_{3}d_{7}}\,
      M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,M_{d_{4}d_{7}}\nl
      \off{3827636}
      +5\,M_{d_{1}d_{3}}\,M_{d_{2}d_{3}}\,M_{d_{3}d_{7}}\,
      M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,M_{d_{6}d_{7}}\nl
      \off{3827636}
      +2\,M_{d_{1}d_{3}}\,M_{d_{2}d_{4}}\,M_{d_{3}d_{4}}\,
      M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,M_{d_{4}d_{7}}\nl
      \off{3827636}
      -8\,M_{d_{1}d_{3}}\,M_{d_{2}d_{6}}\,M_{d_{3}d_{4}}\,
      M_{d_{3}d_{6}}\,M_{d_{4}d_{5}}\,M_{d_{6}d_{7}}\nl
      \off{3827636}
      +2\,M_{d_{1}d_{3}}\,M_{d_{2}d_{6}}\,M_{d_{3}d_{6}}\,
      M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,M_{d_{6}d_{7}}\nl
      \off{3827636}
      -M_{d_{1}d_{3}}\,M_{d_{2}d_{7}}\,M_{d_{3}d_{7}}\,
      M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,M_{d_{4}d_{7}}\nl
      \off{3827636}
      +M_{d_{1}d_{3}}\,M_{d_{2}d_{7}}\,M_{d_{3}d_{7}}\,
      M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,M_{d_{6}d_{7}}
      -2\,M_{d_{1}d_{4}}\,\nl
      \off{3827636}
      M_{d_{2}d_{4}}\,M_{d_{3}d_{4}}\,M_{d_{4}d_{5}}\,
      M_{d_{4}d_{6}}\,M_{d_{4}d_{7}}
      +M_{d_{1}d_{4}}\,M_{d_{2}d_{6}}\,M_{d_{3}d_{4}}\nl
      \off{3827636}
      \,M_{d_{3}d_{6}}\,M_{d_{4}d_{5}}\,M_{d_{6}d_{7}}
      +5\,M_{d_{1}d_{6}}\,M_{d_{2}d_{6}}\,M_{d_{3}d_{4}}\,
      M_{d_{3}d_{6}}\nl
      \off{3827636}
      \,M_{d_{4}d_{5}}\,M_{d_{6}d_{7}}
      -8\,M_{d_{1}d_{6}}\,M_{d_{2}d_{6}}\,M_{d_{3}d_{6}}\,
      M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\nl
      \off{3827636}
      \,M_{d_{6}d_{7}}
      -2\,M_{d_{1}d_{7}}\,M_{d_{2}d_{7}}\,M_{d_{3}d_{6}}\,
      M_{d_{3}d_{7}}\,M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\nl
      \off{3827636}
      +6\,M_{d_{1}d_{7}}\,M_{d_{2}d_{7}}\,M_{d_{3}d_{7}}\,
      M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,M_{d_{4}d_{7}}
      -6\,\nl
      \off{3827636}
      M_{d_{1}d_{7}}\,M_{d_{2}d_{7}}\,M_{d_{3}d_{7}}\,
      M_{d_{4}d_{5}}\,M_{d_{4}d_{6}}\,M_{d_{6}d_{7}}
    \)
  \)
  /60480
\]
\Nl}$$

These expressions are not particularly illuminating but are of interest because they generically do not vanish and hence, define higher order BRST charges. This can be seen by means of the following example, in which only the brackets of the first generator with the other ones are non vanishing, and taken equal to $$\begin{aligned}
\label{eq:maxquad}
[G_1, G_{\alpha}] &=& G_1 G_{\alpha} = - [ G_{\alpha}, G_1]
    \quad  (\alpha = 2,3,\ldots,n),\\{}
[G_{\alpha}, G_{\beta}] &=& 0.\end{aligned}$$ For this particular self-reproducing algebra, all orders of the covariant BRST charge can be explicitly computed. One finds $$\begin{aligned}
{{\renewcommand{\arraystretch}{.7}     \begin{array}[b]{@{}c@{}} {\scriptscriptstyle (0)} \\ \Omega \end{array}}} &=& \eta^a G_a \\
{{\renewcommand{\arraystretch}{.7}     \begin{array}[b]{@{}c@{}} {\scriptscriptstyle (k)} \\ \Omega \end{array}}} &=& \alpha_k ({\renewcommand{\arraystretch}{.7}     