Symmetric Group 7<title> </head> <body> <big style="font-weight: bold;"><big>Group: S7</big></big><span style="font-weight: bold;"><br> Order: 2<sup>4</sup>·3<sup>2</sup>·5·7 <br><br> <table style="text-align: center; vertical-align: middle; width: 100%;" border="1" cellpadding="2" cellspacing="2"> <tbody> <tr> <td>Characteristic</td> <td>Block</td> <td>Dimension</td> <td>Cartan Matrix</td> <td>Generators</td> <td>Links</td> </tr> <tr> <td colspan="1" rowspan="2">2</td> <td>1</td> <td>108</td><td><table style="text-align: left; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align: center;">8</td> <td style="text-align: center;">4</td> <td style="text-align: center;">4</td> </tr> <tr> <td style="text-align: center;">4</td> <td style="text-align: center;">6</td> <td style="text-align: center;">2</td> </tr> <tr> <td style="text-align: center;">4</td> <td style="text-align: center;">2</td> <td style="text-align: center;">4</td> </tr> </tbody> </table> </td> <td>abab^{-1}a, <br>z<sub>11</sub>, z<sub>3</sub>, z<sub>5</sub></td> <td style="font-weight: bold;"><a style="font-weight: normal;" href="S7files/S7mod2b1.html">Condensation Information</a><br> <a style="font-weight: normal;" href="S7files/S7mod2b1extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S7files/S7mod2b1.gap.gz">Basic Algebra</a></td> </tr> <tr> <td>2</td> <td>568</td><td><table style="text-align: left; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align: center;">8</td> <td style="text-align: center;">4</td> </tr> <tr> <td style="text-align: center;">4</td> <td style="text-align: center;">3</td> </tr> </tbody> </table></td> <td>b, bc^{-1}ba, <br>z<sub>11</sub>, z<sub>3</sub></td> <td style="font-weight: bold;"><a style="font-weight: normal;" href="S7files/S7mod2b2.html">Condensation Information</a><br> <a style="font-weight: normal;" href="S7files/S7mod2b2extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S7files/S7mod2b2.gap.gz">Basic Algebra</a></td> </tr> <tr> <td colspan="1" rowspan="3">3</td> <td>1</td> <td>108</td><td><table style="text-align: left; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align: center;">3</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;">1</td> </tr> <tr> <td style="text-align: center;">2</td> <td style="text-align: center;">5</td> <td style="text-align: center;">2</td> <td style="text-align: center;">2</td> <td style="text-align: center;">2</td> </tr> <tr> <td style="text-align: center;">2</td> <td style="text-align: center;">2</td> <td style="text-align: center;">5</td> <td style="text-align: center;">2</td> <td style="text-align: center;">2</td> </tr> <tr> <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;">3</td> <td style="text-align: center;">1</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;">3</td> </tr> </tbody> </table></td> <td>b, <br>z<sub>3</sub>, z<sub>5</sub></td> <td style="font-weight: bold;"><a style="font-weight: normal;" href="S7files/S7mod3b1.html">Condensation Information</a><br> <a style="font-weight: normal;" href="S7files/S7mod3b1extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S7files/S7mod3b1.gap.gz">Basic Algebra</a></td> </tr> <tr> <td>2</td> <td>20</td><td><table style="text-align: left; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align: center;">2</td> <td style="text-align: center;">1</td> </tr> <tr> <td style="text-align: center;">1</td> <td style="text-align: center;">2</td> </tr> </tbody> </table></td> <td>z<sub>4</sub>, z<sub>2</sub></td> <td style="font-weight: bold;"><a style="font-weight: normal;" href="S7files/S7mod3b2.html">Condensation Information</a><br> <a style="font-weight: normal;" href="S7files/S7mod3b2extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S7files/S7mod3b2.gap.gz">Basic Algebra</a></td> </tr> <tr> <td>3</td> <td>56</td><td><table style="text-align: left; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align: center;">2</td> <td style="text-align: center;">1</td> </tr> <tr> <td style="text-align: center;">1</td> <td style="text-align: center;">2</td> </tr> </tbody> </table></td> <td>z<sub>7</sub>, z<sub>11</sub>, z<sub>2</sub></td> <td style="font-weight: bold;"><a style="font-weight: normal;" href="S7files/S7mod3b3.html">Condensation Information</a><br> <a style="font-weight: normal;" href="S7files/S7mod3b3extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S7files/S7mod3b3.gap.gz">Basic Algebra</a></td> </tr> <tr> <td colspan="1" rowspan="2">5</td> <td>1</td> <td>54</td><td><table style="text-align: left; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align: center;">2</td> <td style="text-align: center;">0</td> <td style="text-align: center;">1</td> <td style="text-align: center;">1</td> </tr> <tr> <td style="text-align: center;">0</td> <td style="text-align: center;">2</td> <td style="text-align: center;">1</td> <td style="text-align: center;">0</td> </tr> <tr> <td style="text-align: center;">1</td> <td style="text-align: center;">1</td> <td style="text-align: center;">2</td> <td style="text-align: center;">0</td> </tr> <tr> <td style="text-align: center;">1</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: center;">2</td> </tr> </tbody> </table></td> <td>z<sub>3</sub>, z<sub>6</sub>, z<sub>5</sub></td> <td style="font-weight: bold;"><a style="font-weight: normal;" href="S7files/S7mod5b1.html">Condensation Information</a><br> <a style="font-weight: normal;" href="S7files/S7mod5b1extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S7files/S7mod5b1.gap.gz">Basic Algebra</a></td> </tr> <tr> <td>2</td> <td>54</td><td><table style="text-align: left; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align: center;">2</td> <td style="text-align: center;">0</td> <td style="text-align: center;">1</td> <td style="text-align: center;">1</td> </tr> <tr> <td style="text-align: center;">0</td> <td style="text-align: center;">2</td> <td style="text-align: center;">1</td> <td style="text-align: center;">0</td> </tr> <tr> <td style="text-align: center;">1</td> <td style="text-align: center;">1</td> <td style="text-align: center;">2</td> <td style="text-align: center;">0</td> </tr> <tr> <td style="text-align: center;">1</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: center;">2</td> </tr> </tbody> </table></td> <td>z<sub>3</sub>, z<sub>6</sub>, z<sub>5</sub></td> <td style="font-weight: bold;"><a style="font-weight: normal;" href="S7files/S7mod5b2.html">Condensation Information</a><br> <a style="font-weight: normal;" href="S7files/S7mod5b2extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S7files/S7mod5b2.gap.gz">Basic Algebra</a></td> </tr> <tr> <td colspan="1" rowspan="1">7</td> <td>1</td> <td>70</td><td><table style="text-align: left; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align: center;">2</td> <td style="text-align: center;">1</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: center;">1</td> <td style="text-align: center;">0</td> </tr> <tr> <td style="text-align: center;">1</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;">0</td> <td style="text-align: center;">1</td> </tr> <tr> <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;">0</td> <td style="text-align: center;">1</td> <td style="text-align: center;">0</td> </tr> <tr> <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;">0</td> <td style="text-align: center;">1</td> </tr> <tr> <td style="text-align: center;">1</td> <td style="text-align: center;">0</td> <td style="text-align: center;">1</td> <td style="text-align: center;">0</td> <td style="text-align: center;">2</td> <td style="text-align: center;">0</td> </tr> <tr> <td style="text-align: center;">0</td> <td style="text-align: center;">1</td> <td style="text-align: center;">0</td> <td style="text-align: center;">1</td> <td style="text-align: center;">0</td> <td style="text-align: center;">2</td> </tr> </tbody> </table></td> <td>z<sub>5</sub>, z<sub>7</sub>, z<sub>4</sub>,<br>z<sub>8</sub></td> <td style="font-weight: bold;"><a style="font-weight: normal;" href="S7files/S7mod7b1.html">Condensation Information</a><br> <a style="font-weight: normal;" href="S7files/S7mod7b1extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S7files/S7mod7b1.gap.gz">Basic Algebra</a></td> </tr> </tbody> </table> </body> </html>