Mathieu Group M11 Condensation Information<title> </head> <body> <big style="font-weight: bold;"><big>Information about faithful condensation of block 1 for M11 in characteristic 3</big></big><br> <p> Faithful condensation using the 6-th subgroup. The order of this subgroup is 5. <br> This subgroup was constructed as the subgroup generated by <br><p><b^{-1}ab^{-1}><br><p> inside its normalizer, the 21-th subgroup.<br> <p> The corresponding permutation character is: <br> <p> <table cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="text-align: center;">1584</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: center;">4</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> </tr> </tbody> </table><p> The dimensions of the modular irreducibles and their condensed dimensions are: <br> <p> <table cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="text-align: center;">1</td> <td style="text-align: center;">5</td> <td style="text-align: center;">5</td> <td style="text-align: center;">10</td> <td style="text-align: center;">10</td> <td style="text-align: center;">10</td> <td style="text-align: center;">24</td> </tr> <tr> <td style="text-align: center;">1</td> <td style="text-align: center;">1</td> <td style="text-align: center;">1</td> <td style="text-align: center;">2</td> <td style="text-align: center;">2</td> <td style="text-align: center;">2</td> <td style="text-align: center;">4</td> </tr> </tbody> </table><p> The dimensions of the projective indecomposable modules and their condensed dimensions are: <br> <p> <table cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="text-align: center;">99</td> <td style="text-align: center;">126</td> <td style="text-align: center;">126</td> <td style="text-align: center;">54</td> <td style="text-align: center;">81</td> <td style="text-align: center;">81</td> <td style="text-align: center;">99</td> </tr> <tr> <td style="text-align: center;">23</td> <td style="text-align: center;">26</td> <td style="text-align: center;">26</td> <td style="text-align: center;">10</td> <td style="text-align: center;">17</td> <td style="text-align: center;">17</td> <td style="text-align: center;">19</td> </tr> </tbody> </table> </body> </html>