Suzuki Group Sz(8) Condensation Information<title> </head> <body> <big style="font-weight: bold;"><big>Information about faithful condensation of block 1 for Sz(8) in characteristic 7</big></big><br> <p> Faithful condensation using the 20-th subgroup. The order of this subgroup is 64. <br> This subgroup was constructed as the subgroup generated by <br><p><ba^{-1}b^{-1}a, aba^{-1}b^{-1}, ba^{-2}b^{-1}a^{2}, a^{2}b^{2}a^{-2}, a^{-1}b^{2}a^{-1}b^{2}a^{2}, b^{2}a^{-1}b^{2}a><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;">455</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;">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> <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;">64</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;">196</td> <td style="text-align: center;">259</td> </tr> <tr> <td style="text-align: center;">7</td> <td style="text-align: center;">7</td> </tr> </tbody> </table> </body> </html>