Linear representation theory of alternating group:A9

This article gives specific information, namely, linear representation theory, about a particular group, namely: alternating group:A9.
View linear representation theory of particular groups | View other specific information about alternating group:A9

Summary

Item	Value
degrees of irreducible representations over a splitting field (such as $\bar{Q}$ or $C$ )	1, 8, 21, 21, 27, 28, 35, 35, 42, 48, 56, 84, 105, 120, 162, 168, 189, 216 grouped form (each occurs once by default): 1, 8, 21 (2 times), 27, 28, 35 (2 times), 42, 48, 56, 84, 105, 120, 162, 168, 189, 216 maximum: 216, number: 18, sum of squares: 181440

GAP implementation

Degrees of irreducible representations

These can be computed using the CharacterDegrees function:

gap> CharacterDegrees(CharacterTable(AlternatingGroup(9)));
[ [ 1, 1 ], [ 8, 1 ], [ 21, 2 ], [ 27, 1 ], [ 28, 1 ], [ 35, 2 ], [ 42, 1 ], [ 48, 1 ], [ 56, 1 ], [ 84, 1 ], [ 105, 1 ], [ 120, 1 ], [ 162, 1 ],
  [ 168, 1 ], [ 189, 1 ], [ 216, 1 ] ]