Symmetric Group 5<title> </head> <body> <big style="font-weight: bold;"><big>Group: S5</big></big><span style="font-weight: bold;"><br> Order: 2<sup>3</sup>·3·5 <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>120</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>(1,2), (2,3,4,5)<td style="font-weight: bold;"><a style="font-weight: normal;" href="<a style="font-weight: normal;" href="S5files/S5mod2b1extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S5files/S5mod2b1.gap.gz">Basic Algebra</a></td> </tr> <tr> <td>2</td> <td>16</td><td><table style="text-align: left; margin-left: auto; margin-right: auto;"> <tbody> <tr> <td style="text-align: center;">2</td> </tr> </tbody> </table></td> <td>bc, a, <br>z<sub>2</sub>, z<sub>4</sub></td> <td style="font-weight: bold;"><a style="font-weight: normal;" href="S5files/S5mod2b2.html">Condensation Information</a><br> <a style="font-weight: normal;" href="S5files/S5mod2b2extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S5files/S5mod2b2.gap.gz">Basic Algebra</a></td> </tr> <tr> <td colspan="1" rowspan="2">3</td> <td>1</td> <td>9</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>1</sub>, z<sub>4</sub></td> <td style="font-weight: bold;"><a style="font-weight: normal;" href="S5files/S5mod3b1.html">Condensation Information</a><br> <a style="font-weight: normal;" href="S5files/S5mod3b1extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S5files/S5mod3b1.gap.gz">Basic Algebra</a></td> </tr> <tr> <td>2</td> <td>12</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>a, <br>z<sub>1</sub>, z<sub>2</sub></td> <td style="font-weight: bold;"><a style="font-weight: normal;" href="S5files/S5mod3b2.html">Condensation Information</a><br> <a style="font-weight: normal;" href="S5files/S5mod3b2extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S5files/S5mod3b2.gap.gz">Basic Algebra</a></td> </tr> <tr> <td colspan="1" rowspan="1">5</td> <td>1</td> <td>16</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> </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;">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;">1</td> </tr> <tr> <td style="text-align: center;">0</td> <td style="text-align: center;">1</td> <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="S5files/S5mod5b1.html">Condensation Information</a><br> <a style="font-weight: normal;" href="S5files/S5mod5b1extdim.html">Ext Dimensions</a><br> <a style="font-weight: normal;" href="S5files/S5mod5b1.gap.gz">Basic Algebra</a></td> </tr> </tbody> </table> </body> </html>