Linear Group L3(4) Condensation Information<title> </head> <body> <big style="font-weight: bold;"><big>Information about faithful condensation of block 1 for L3(4) in characteristic 2</big></big><br> <p> Faithful condensation using the 14-th subgroup. The order of this subgroup is 5. <br> This subgroup was constructed as the subgroup generated by <br><p><ab><br><p> inside its normalizer, the 27-th subgroup.<br> <p> The corresponding permutation character is: <br> <p> <table cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="text-align: center;">4032</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> <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;">8</td> <td style="text-align: center;">8</td> <td style="text-align: center;">9</td> <td style="text-align: center;">9</td> </tr> <tr> <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;">1</td> <td style="text-align: center;">1</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;">704</td> <td style="text-align: center;">384</td> <td style="text-align: center;">384</td> <td style="text-align: center;">512</td> <td style="text-align: center;">512</td> </tr> <tr> <td style="text-align: center;">144</td> <td style="text-align: center;">78</td> <td style="text-align: center;">78</td> <td style="text-align: center;">104</td> <td style="text-align: center;">104</td> </tr> </tbody> </table> </body> </html>