Difference between revisions of "M(32,51,22)"

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M(32,51,22) - $k((C_2)^4 : C_{31})$
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Representative: $k((C_2)^4 : C_{15}) \times C_2)$ $(C_2)^5$ $C_{31}$ 32 31 1 See below. Yes Yes Yes $\mathcal{O} ((C_2)^5 : C_{31})$ See below. 1 No Yes M(32,51,23) Yes

Covering blocks and covered blocks

Let $N \triangleleft G$ with prime $p'$-index and let $B$ be a block of $\mathcal{O} G$ covering a block $b$ of $\mathcal{O} N$.

If $b$ is in M(32,51,22), then $B$ is in M(32,51,1), M(32,51,22) or M(32,51,30).

Projective indecomposable modules

Labelling the simple $B$-modules by $S_1, \dots, S_{31}$, the projective indecomposable modules have Loewy structure as follows:

$\begin{array}{ccccc} \begin{array}{c} S_{1} \\ S_{8} S_{11} S_{9} S_{7} S_{10} \\ S_{13} S_{17} S_{18} S_{15} S_{5} S_{6} S_{14} S_{19} S_{16} S_{12} \\ S_{24} S_{23} S_{21} S_{4} S_{22} S_{3} S_{27} S_{25} S_{20} S_{26} \\ S_{30} S_{2} S_{29} S_{31} S_{28} \\ S_{1} \\ \end{array} & \begin{array}{c} S_{2} \\ S_{8} S_{1} S_{26} S_{17} S_{31} \\ S_{21} S_{25} S_{16} S_{30} S_{9} S_{11} S_{7} S_{14} S_{12} S_{10} \\ S_{20} S_{24} S_{23} S_{13} S_{29} S_{19} S_{15} S_{18} S_{5} S_{6} \\ S_{4} S_{3} S_{27} S_{28} S_{22} \\ S_{2} \\ \end{array} & \begin{array}{c} S_{3} \\ S_{2} S_{8} S_{23} S_{14} S_{28} \\ S_{1} S_{16} S_{12} S_{17} S_{9} S_{26} S_{27} S_{20} S_{18} S_{31} \\ S_{10} S_{30} S_{15} S_{7} S_{25} S_{22} S_{13} S_{11} S_{21} S_{24} \\ S_{19} S_{4} S_{6} S_{5} S_{29} \\ S_{3} \\ \end{array} & \begin{array}{c} S_{4} \\ S_{21} S_{3} S_{29} S_{17} S_{2} \\ S_{1} S_{23} S_{31} S_{19} S_{25} S_{10} S_{26} S_{8} S_{14} S_{28} \\ S_{6} S_{12} S_{30} S_{9} S_{16} S_{7} S_{27} S_{18} S_{11} S_{20} \\ S_{15} S_{13} S_{5} S_{24} S_{22} \\ S_{4} \\ \end{array} & \begin{array}{c} S_{5} \\ S_{3} S_{24} S_{8} S_{12} S_{4} \\ S_{15} S_{2} S_{16} S_{14} S_{29} S_{21} S_{17} S_{28} S_{23} S_{9} \\ S_{25} S_{19} S_{1} S_{31} S_{10} S_{18} S_{13} S_{27} S_{26} S_{20} \\ S_{30} S_{6} S_{11} S_{22} S_{7} \\ S_{5} \\ \end{array} \end{array}$

$\begin{array}{ccccc} \begin{array}{c} S_{6} \\ S_{20} S_{22} S_{14} S_{3} S_{5} \\ S_{4} S_{8} S_{23} S_{2} S_{30} S_{28} S_{26} S_{12} S_{24} S_{18} \\ S_{15} S_{21} S_{16} S_{29} S_{9} S_{1} S_{27} S_{17} S_{31} S_{11} \\ S_{13} S_{19} S_{7} S_{10} S_{25} \\ S_{6} \\ \end{array} & \begin{array}{c} S_{7} \\ S_{16} S_{5} S_{6} S_{13} S_{8} \\ S_{9} S_{14} S_{24} S_{4} S_{17} S_{3} S_{22} S_{20} S_{12} S_{25} \\ S_{26} S_{15} S_{30} S_{10} S_{23} S_{18} S_{28} S_{21} S_{2} S_{29} \\ S_{31} S_{19} S_{11} S_{27} S_{1} \\ S_{7} \\ \end{array} & \begin{array}{c} S_{8} \\ S_{9} S_{16} S_{14} S_{12} S_{17} \\ S_{25} S_{21} S_{20} S_{10} S_{18} S_{23} S_{13} S_{26} S_{24} S_{15} \\ S_{6} S_{28} S_{19} S_{4} S_{30} S_{11} S_{31} S_{22} S_{27} S_{29} \\ S_{3} S_{1} S_{2} S_{5} S_{7} \\ S_{8} \\ \end{array} & \begin{array}{c} S_{9} \\ S_{13} S_{17} S_{10} S_{18} S_{15} \\ S_{27} S_{22} S_{21} S_{6} S_{11} S_{25} S_{19} S_{14} S_{4} S_{26} \\ S_{31} S_{5} S_{20} S_{2} S_{29} S_{30} S_{3} S_{23} S_{7} S_{12} \\ S_{8} S_{24} S_{28} S_{16} S_{1} \\ S_{9} \\ \end{array} & \begin{array}{c} S_{10} \\ S_{14} S_{6} S_{18} S_{19} S_{11} \\ S_{23} S_{12} S_{3} S_{27} S_{20} S_{22} S_{7} S_{26} S_{5} S_{15} \\ S_{4} S_{30} S_{16} S_{31} S_{28} S_{24} S_{8} S_{13} S_{2} S_{21} \\ S_{1} S_{29} S_{25} S_{17} S_{9} \\ S_{10} \\ \end{array} \end{array}$

$\begin{array}{ccccc} \begin{array}{c} S_{11} \\ S_{12} S_{15} S_{5} S_{7} S_{19} \\ S_{27} S_{23} S_{13} S_{4} S_{21} S_{24} S_{8} S_{3} S_{6} S_{16} \\ S_{9} S_{20} S_{29} S_{22} S_{25} S_{17} S_{14} S_{28} S_{2} S_{31} \\ S_{26} S_{30} S_{1} S_{10} S_{18} \\ S_{11} \\ \end{array} & \begin{array}{c} S_{12} \\ S_{16} S_{15} S_{23} S_{24} S_{21} \\ S_{9} S_{25} S_{19} S_{29} S_{13} S_{20} S_{28} S_{31} S_{4} S_{27} \\ S_{6} S_{30} S_{7} S_{2} S_{17} S_{22} S_{3} S_{10} S_{1} S_{18} \\ S_{11} S_{14} S_{26} S_{5} S_{8} \\ S_{12} \\ \end{array} & \begin{array}{c} S_{13} \\ S_{22} S_{25} S_{6} S_{4} S_{17} \\ S_{21} S_{10} S_{29} S_{30} S_{20} S_{3} S_{26} S_{5} S_{2} S_{14} \\ S_{31} S_{8} S_{19} S_{11} S_{23} S_{24} S_{18} S_{28} S_{12} S_{1} \\ S_{15} S_{27} S_{16} S_{7} S_{9} \\ S_{13} \\ \end{array} & \begin{array}{c} S_{14} \\ S_{20} S_{26} S_{23} S_{18} S_{12} \\ S_{22} S_{15} S_{24} S_{16} S_{11} S_{31} S_{27} S_{30} S_{21} S_{28} \\ S_{4} S_{19} S_{25} S_{7} S_{13} S_{2} S_{29} S_{1} S_{9} S_{5} \\ S_{6} S_{10} S_{8} S_{3} S_{17} \\ S_{14} \\ \end{array} & \begin{array}{c} S_{15} \\ S_{27} S_{21} S_{13} S_{19} S_{4} \\ S_{22} S_{3} S_{29} S_{2} S_{25} S_{17} S_{31} S_{23} S_{6} S_{7} \\ S_{14} S_{1} S_{30} S_{5} S_{28} S_{8} S_{16} S_{20} S_{26} S_{10} \\ S_{12} S_{18} S_{9} S_{11} S_{24} \\ S_{15} \\ \end{array} \end{array}$

$\begin{array}{ccccc} \begin{array}{c} S_{16} \\ S_{9} S_{24} S_{25} S_{20} S_{13} \\ S_{30} S_{18} S_{4} S_{29} S_{22} S_{28} S_{17} S_{15} S_{6} S_{10} \\ S_{19} S_{11} S_{2} S_{26} S_{27} S_{3} S_{21} S_{14} S_{1} S_{5} \\ S_{7} S_{23} S_{8} S_{12} S_{31} \\ S_{16} \\ \end{array} & \begin{array}{c} S_{17} \\ S_{10} S_{14} S_{25} S_{26} S_{21} \\ S_{18} S_{30} S_{6} S_{23} S_{20} S_{12} S_{11} S_{29} S_{19} S_{31} \\ S_{3} S_{7} S_{1} S_{5} S_{27} S_{22} S_{28} S_{16} S_{15} S_{24} \\ S_{2} S_{13} S_{9} S_{8} S_{4} \\ S_{17} \\ \end{array} & \begin{array}{c} S_{18} \\ S_{22} S_{26} S_{11} S_{27} S_{15} \\ S_{7} S_{2} S_{13} S_{21} S_{4} S_{5} S_{19} S_{31} S_{30} S_{12} \\ S_{8} S_{29} S_{6} S_{25} S_{16} S_{24} S_{23} S_{17} S_{1} S_{3} \\ S_{10} S_{20} S_{28} S_{14} S_{9} \\ S_{18} \\ \end{array} & \begin{array}{c} S_{19} \\ S_{23} S_{3} S_{7} S_{27} S_{6} \\ S_{13} S_{8} S_{20} S_{16} S_{14} S_{22} S_{28} S_{31} S_{5} S_{2} \\ S_{18} S_{4} S_{1} S_{26} S_{17} S_{12} S_{25} S_{9} S_{24} S_{30} \\ S_{10} S_{11} S_{29} S_{15} S_{21} \\ S_{19} \\ \end{array} & \begin{array}{c} S_{20} \\ S_{30} S_{18} S_{24} S_{22} S_{28} \\ S_{4} S_{9} S_{2} S_{15} S_{5} S_{26} S_{11} S_{1} S_{27} S_{29} \\ S_{17} S_{8} S_{31} S_{12} S_{13} S_{19} S_{21} S_{10} S_{3} S_{7} \\ S_{25} S_{23} S_{16} S_{14} S_{6} \\ S_{20} \\ \end{array} \end{array}$

$\begin{array}{ccccc} \begin{array}{c} S_{21} \\ S_{29} S_{19} S_{23} S_{25} S_{31} \\ S_{1} S_{6} S_{20} S_{27} S_{28} S_{30} S_{7} S_{16} S_{10} S_{3} \\ S_{14} S_{18} S_{22} S_{13} S_{8} S_{24} S_{9} S_{11} S_{2} S_{5} \\ S_{26} S_{4} S_{15} S_{17} S_{12} \\ S_{21} \\ \end{array} & \begin{array}{c} S_{22} \\ S_{4} S_{5} S_{30} S_{26} S_{2} \\ S_{3} S_{11} S_{24} S_{12} S_{21} S_{1} S_{29} S_{31} S_{8} S_{17} \\ S_{9} S_{10} S_{28} S_{14} S_{15} S_{25} S_{16} S_{23} S_{19} S_{7} \\ S_{27} S_{18} S_{6} S_{20} S_{13} \\ S_{22} \\ \end{array} & \begin{array}{c} S_{23} \\ S_{27} S_{16} S_{28} S_{20} S_{31} \\ S_{30} S_{18} S_{2} S_{24} S_{13} S_{1} S_{9} S_{25} S_{7} S_{22} \\ S_{5} S_{11} S_{4} S_{26} S_{29} S_{10} S_{15} S_{8} S_{17} S_{6} \\ S_{3} S_{12} S_{14} S_{19} S_{21} \\ S_{23} \\ \end{array} & \begin{array}{c} S_{24} \\ S_{15} S_{28} S_{9} S_{29} S_{4} \\ S_{13} S_{3} S_{2} S_{10} S_{18} S_{19} S_{1} S_{17} S_{21} S_{27} \\ S_{6} S_{31} S_{8} S_{26} S_{22} S_{23} S_{14} S_{25} S_{7} S_{11} \\ S_{5} S_{20} S_{16} S_{12} S_{30} \\ S_{24} \\ \end{array} & \begin{array}{c} S_{25} \\ S_{30} S_{10} S_{20} S_{6} S_{29} \\ S_{11} S_{19} S_{24} S_{14} S_{1} S_{28} S_{22} S_{18} S_{5} S_{3} \\ S_{8} S_{2} S_{12} S_{26} S_{15} S_{23} S_{7} S_{9} S_{4} S_{27} \\ S_{31} S_{21} S_{13} S_{17} S_{16} \\ S_{25} \\ \end{array} \end{array}$

$\begin{array}{ccccc} \begin{array}{c} S_{26} \\ S_{11} S_{12} S_{31} S_{21} S_{30} \\ S_{23} S_{15} S_{25} S_{16} S_{29} S_{7} S_{5} S_{19} S_{1} S_{24} \\ S_{9} S_{8} S_{27} S_{28} S_{3} S_{13} S_{6} S_{4} S_{10} S_{20} \\ S_{22} S_{2} S_{17} S_{18} S_{14} \\ S_{26} \\ \end{array} & \begin{array}{c} S_{27} \\ S_{31} S_{22} S_{2} S_{13} S_{7} \\ S_{1} S_{8} S_{25} S_{17} S_{6} S_{4} S_{26} S_{16} S_{30} S_{5} \\ S_{12} S_{3} S_{20} S_{9} S_{14} S_{21} S_{29} S_{24} S_{11} S_{10} \\ S_{28} S_{23} S_{15} S_{18} S_{19} \\ S_{27} \\ \end{array} & \begin{array}{c} S_{28} \\ S_{18} S_{2} S_{27} S_{9} S_{1} \\ S_{15} S_{7} S_{31} S_{22} S_{13} S_{10} S_{17} S_{11} S_{26} S_{8} \\ S_{21} S_{4} S_{5} S_{30} S_{12} S_{6} S_{19} S_{14} S_{25} S_{16} \\ S_{24} S_{29} S_{3} S_{20} S_{23} \\ S_{28} \\ \end{array} & \begin{array}{c} S_{29} \\ S_{3} S_{19} S_{10} S_{1} S_{28} \\ S_{6} S_{18} S_{7} S_{11} S_{8} S_{2} S_{14} S_{23} S_{9} S_{27} \\ S_{26} S_{17} S_{5} S_{20} S_{16} S_{31} S_{15} S_{13} S_{22} S_{12} \\ S_{25} S_{4} S_{21} S_{24} S_{30} \\ S_{29} \\ \end{array} & \begin{array}{c} S_{30} \\ S_{11} S_{1} S_{24} S_{5} S_{29} \\ S_{3} S_{7} S_{15} S_{12} S_{19} S_{9} S_{8} S_{10} S_{28} S_{4} \\ S_{6} S_{23} S_{16} S_{14} S_{2} S_{21} S_{27} S_{17} S_{18} S_{13} \\ S_{26} S_{31} S_{25} S_{22} S_{20} \\ S_{30} \\ \end{array} & \begin{array}{c} S_{31} \\ S_{7} S_{30} S_{1} S_{16} S_{25} \\ S_{5} S_{13} S_{20} S_{10} S_{6} S_{8} S_{9} S_{29} S_{24} S_{11} \\ S_{28} S_{22} S_{18} S_{15} S_{4} S_{14} S_{12} S_{19} S_{3} S_{17} \\ S_{27} S_{23} S_{2} S_{26} S_{21} \\ S_{31} \\ \end{array} \end{array}$

Irreducible characters

All irreducible characters have height zero.

Cartan matrix

$\left( \begin{array}{ccccccccccccccccccccccccccccccc} 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 2 \end{array} \right)$

Decomposition matrix

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