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 11</big></big><br> <p> Faithful condensation using the 11-th subgroup. The order of this subgroup is 8. <br> This subgroup was constructed as the subgroup generated by <br><p><b^{2}, baba, b^{-1}a><br><p> inside its normalizer, the 18-th subgroup.<br> <p> The corresponding permutation character is: <br> <p> <table cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="text-align: center;">990</td> <td style="text-align: center;">6</td> <td style="text-align: center;">0</td> <td style="text-align: center;">2</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: center;">2</td> <td style="text-align: center;">2</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;">9</td> <td style="text-align: center;">10</td> <td style="text-align: center;">10</td> <td style="text-align: center;">16</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;">1</td> <td style="text-align: center;">2</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;">11</td> <td style="text-align: center;">55</td> <td style="text-align: center;">55</td> <td style="text-align: center;">55</td> <td style="text-align: center;">77</td> </tr> <tr> <td style="text-align: center;">3</td> <td style="text-align: center;">7</td> <td style="text-align: center;">6</td> <td style="text-align: center;">6</td> <td style="text-align: center;">9</td> </tr> </tbody> </table> </body> </html>