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 3</big></big><br> <p> Faithful condensation using the 47-th subgroup. The order of this subgroup is 16. <br> This subgroup was constructed as the subgroup generated by <br><p><b^{2}, baba, abc, db><br><p> inside its normalizer, the 78-th subgroup.<br> <p> The corresponding permutation character is: <br> <p> <table cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="text-align: center;">1260</td> <td style="text-align: center;">12</td> <td style="text-align: center;">0</td> <td style="text-align: center;">4</td> <td style="text-align: center;">4</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> </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;">15</td> <td style="text-align: center;">15</td> <td style="text-align: center;">15</td> <td style="text-align: center;">19</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;">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;">126</td> <td style="text-align: center;">99</td> <td style="text-align: center;">99</td> <td style="text-align: center;">99</td> <td style="text-align: center;">189</td> </tr> <tr> <td style="text-align: center;">12</td> <td style="text-align: center;">7</td> <td style="text-align: center;">7</td> <td style="text-align: center;">7</td> <td style="text-align: center;">15</td> </tr> </tbody> </table> </body> </html>