Difference between revisions of "Linear representation theory of monster group"

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| [[degrees of irreducible representations]] || (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
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| [[degrees of irreducible representations]] over a [[splitting field]] (such as <math>\overline{\mathbb{Q}}</math> or <math>\mathbb{C}</math>) || (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
 
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==External links==
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* {{atlas|M}}
 
==GAP implementation==
 
==GAP implementation==
  

Latest revision as of 21:45, 31 March 2012

This article gives specific information, namely, linear representation theory, about a particular group, namely: monster group.
View linear representation theory of particular groups | View other specific information about monster group

Summary

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)
number: 194, sum of squares: 808017424794512875886459904961710757005754368000000000, maximum degree of irreducible representation: 258823477531055064045234375, quasirandom degree: 196883

External links

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 CharacterDegrees and CharacterTable functions.

gap> CharacterDegrees(CharacterTable("M"));
[ [ 1, 1 ], [ 196883, 1 ], [ 21296876, 1 ], [ 842609326, 1 ], [ 18538750076, 1 ], [ 19360062527, 1 ], [ 293553734298, 1 ], [ 3879214937598, 1 ],
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