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## Linear representation theory of monster group

, 21:45, 31 March 2012
no edit summary
group = monster group|
connective = of}}

==Summary==

{| class="sortable" border="1"
! Item !! Value
|-
| [[degrees of irreducible representations]] over a [[splitting field]] (such as $\overline{\mathbb{Q}}$ or $\mathbb{C}$) || (too long to list -- see [[#GAP implementation]])<br>[[number of irreducible representations equals number of conjugacy classes|number]]: 194, [[sum of squares of degrees of irreducible representations equals order of group|sum of squares]]: 808017424794512875886459904961710757005754368000000000, [[maximum degree of irreducible representation]]: 258823477531055064045234375, [[quasirandom degree]]: 196883
|}

==External links==

* {{atlas|M}}
==GAP implementation==

===Degrees of irreducible representations===

The monster group itself is not stored in GAP, but some information on its irreducible representations is, and we use the symbol "M" to access this information. The degrees of irreducible representations can be computed using the [[GAP:CharacterDegrees|CharacterDegrees]] and [[GAP:CharacterTable|CharacterTable]] functions.

<pre>gap> CharacterDegrees(CharacterTable("M"));
[ [ 1, 1 ], [ 196883, 1 ], [ 21296876, 1 ], [ 842609326, 1 ], [ 18538750076, 1 ], [ 19360062527, 1 ], [ 293553734298, 1 ], [ 3879214937598, 1 ],
[ 36173193327999, 1 ], [ 125510727015275, 1 ], [ 190292345709543, 1 ], [ 222879856734249, 1 ], [ 1044868466775133, 1 ], [ 1109944460516150, 1 ],
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[ 241866941438795926688759808, 1 ], [ 258823477531055064045234375, 1 ] ]</pre>
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