Linear representation theory of monster group
From Groupprops
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 ![]() ![]() |
(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 ], [ 36173193327999, 1 ], [ 125510727015275, 1 ], [ 190292345709543, 1 ], [ 222879856734249, 1 ], [ 1044868466775133, 1 ], [ 1109944460516150, 1 ], [ 2374124840062976, 1 ], [ 8980616927734375, 2 ], [ 15178147608537368, 1 ], [ 39660520552077425, 1 ], [ 60359800576579350, 1 ], [ 251098487132187500, 1 ], [ 290568421805921077, 1 ], [ 336041615485626050, 1 ], [ 2500435234254428856, 1 ], [ 2986480825407204125, 1 ], [ 3503434660075044981, 2 ], [ 3605718753596953125, 1 ], [ 8456836343580310400, 1 ], [ 8754193822112578125, 1 ], [ 28585990950721640625, 1 ], [ 30815545786259524745, 1 ], [ 31569817307122699605, 1 ], [ 47377503606648784400, 1 ], [ 49609712911192813665, 1 ], [ 77316619273928125000, 1 ], [ 130415350420342968750, 1 ], [ 155943076739182582850, 1 ], [ 172399434201593354756, 2 ], [ 286243267692724486144, 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