# Linear representation theory of monster group

View linear representation theory of particular groups | View other specific information about monster group

## Summary

Item Value
degrees of irreducible representations (too long to list -- see #GAP implementation)
number: 194, sum of squares of degrees of irreducible representations equals order of group: 808017424794512875886459904961710757005754368000000000, maximum degree of irreducible representation: 258823477531055064045234375, quasirandom degree: 196883

## 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 ],
[ 36173193327999, 1 ], [ 125510727015275, 1 ], [ 190292345709543, 1 ], [ 222879856734249, 1 ], [ 1044868466775133, 1 ], [ 1109944460516150, 1 ],
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