M(32,51,22) - Revision history

CesareGArdito: Created page with "{{blockbox |title = M(32,51,22) - $k((C_2)^4 : C_{31})$ |image = |representative = $k((C_2)^4 : C_{15}) \times C_2)$ |defect = (C2)%5E5|
2019-12-09T11:59:37Z

Created page with "{{blockbox |title = M(32,51,22) - <math>k((C_2)^4 : C_{31})</math> |image = |representative = <math>k((C_2)^4 : C_{15}) \times C_2)</math> |defect = (C2)%5E5|<math..."

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{{blockbox
|title = M(32,51,22) - <math>k((C_2)^4 : C_{31})</math>
|image =  
|representative = <math>k((C_2)^4 : C_{15}) \times C_2)</math>
|defect = [[(C2)%5E5|<math>(C_2)^5</math>]]
|inertialquotients = <math>C_{31}</math>
|k(B) = 32
|l(B) = 31
|k-morita-frob = 1
|Pic-k=  
|cartan = See below.
|defect-morita-inv? = Yes
|inertial-morita-inv? = Yes
|O-morita? = Yes
|O-morita = <math>\mathcal{O} ((C_2)^5 : C_{31})</math>
|decomp = See below.
|O-morita-frob = 1
|Pic-O =
|PIgroup =
|source? = No
|sourcereps =
|k-derived-known? = Yes
|k-derived = [[M(32,51,23)]]
|O-derived-known? = Yes
|coveringblocks =
|coveredblocks =
|pcoveringblocks =
}}

== Basic algebra ==

== Other notatable representatives ==

== Covering blocks and covered blocks ==

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

If <math>b</math> is in M(32,51,22), then <math>B</math> is in [[M(32,51,1)]], M(32,51,22) or [[M(32,51,30)]].

== Projective indecomposable modules ==

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

<math>\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}
</math>

<br>  <br>

<math>\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}
</math>

<br>  <br>

<math>\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}
</math>

<br>  <br>

<math>\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}
</math>

<br>  <br>

<math>\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}
</math>

<br>  <br>

<math>\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}
</math>

== Irreducible characters ==

All irreducible characters have height zero.

== Cartan matrix ==
<math>\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)</math>

== Decomposition matrix ==

<math>\left( \begin{array}{ccccccccccccccccccccccccccccccc}
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
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\end{array}\right)</math>

[[(C2)%5E5|Back to <math>(C_2)^5</math>]]