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 5</big></big><br> <p> Faithful condensation using the 70-th subgroup. The order of this subgroup is 48. <br> This subgroup was constructed as the subgroup generated by <br><p><a, b><br><p> inside its normalizer, the 70-th subgroup.<br> <p> The corresponding permutation character is: <br> <p> <table cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="text-align: center;">420</td> <td style="text-align: center;">4</td> <td style="text-align: center;">6</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> <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;">63</td> </tr> <tr> <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;">65</td> <td style="text-align: center;">190</td> </tr> <tr> <td style="text-align: center;">3</td> <td style="text-align: center;">4</td> </tr> </tbody> </table> </body> </html>