Linear representation theory of monster group

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 ], [ 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