Linear representation theory of Higman-Sims group

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

Summary

Item	Value
degrees of irreducible representations over a splitting field (such as ${\overline {\mathbb {Q} }}$ or $\mathbb {C}$)	1, 22, 77, 154 (3 times), 175, 231, 693, 770 (3 times), 825, 896 (2 times), 1056, 1386, 1408, 1750, 1925 (2 times), 2520, 2750, 3200 number: 24, quasirandom degree: 22, maximum: 3200, sum of squares: 44352000

External links

• HS on the Atlas of Finite Groups

GAP implementation

Some information on its irreducible representations is available on GAP, and we use the symbol "HS" to access this information. The degrees of irreducible representations can be computed using the CharacterDegrees and CharacterTable functions.

gap> CharacterDegrees(CharacterTable("HS"));
[ [ 1, 1 ], [ 22, 1 ], [ 77, 1 ], [ 154, 3 ], [ 175, 1 ], [ 231, 1 ],
  [ 693, 1 ], [ 770, 3 ], [ 825, 1 ], [ 896, 2 ], [ 1056, 1 ], [ 1386, 1 ],
  [ 1408, 1 ], [ 1750, 1 ], [ 1925, 2 ], [ 2520, 1 ], [ 2750, 1 ],
  [ 3200, 1 ] ]