Linear representation theory of Harada-Norton group

This article gives specific information, namely, linear representation theory, about a particular group, namely: Harada-Norton group.
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Summary

Item

Value

degrees of irreducible representations over a splitting field (such as ${\overline {\mathbb {Q} }}$ or $\mathbb {C}$)

1, 133 (2 times), 760, 3344, 8778 (2 times), 8910, 9405, 16929, 35112 (2 times), 65835 (2 times), 69255 (2 times), 214016, 267520, 270864, 365750, 374528 (2 times), 406296, 653125, 656250 (2 times), 718200 (2 times), 1053360, 1066527 (2 times), 1185030 1354320, 1361920 (3 times), 1575936, 1625184, 2031480, 2375000, 2407680, 2661120, 2784375, 2985984, 3200000, 3424256, 3878280, 4156250, 4561920, 4809375, 5103000 (2 times), 5332635, 5878125 number: 54, quasirandom degree: 133, maximum: 5878125, sum of squares: 273030912000000

External links

• HN on the Atlas of Finite Groups

GAP implementation

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

gap> CharacterDegrees(CharacterTable("HN"));
[ [ 1, 1 ], [ 133, 2 ], [ 760, 1 ], [ 3344, 1 ], [ 8778, 2 ], [ 8910, 1 ], [ 9405, 1 ], [ 16929, 1 ], [ 35112, 2 ], [ 65835, 2 ], [ 69255, 2 ],
  [ 214016, 1 ], [ 267520, 1 ], [ 270864, 1 ], [ 365750, 1 ], [ 374528, 2 ], [ 406296, 1 ], [ 653125, 1 ], [ 656250, 2 ], [ 718200, 2 ], [ 1053360, 1 ],
  [ 1066527, 2 ], [ 1185030, 1 ], [ 1354320, 1 ], [ 1361920, 3 ], [ 1575936, 1 ], [ 1625184, 1 ], [ 2031480, 1 ], [ 2375000, 1 ], [ 2407680, 1 ],
  [ 2661120, 1 ], [ 2784375, 1 ], [ 2985984, 1 ], [ 3200000, 1 ], [ 3424256, 1 ], [ 3878280, 1 ], [ 4156250, 1 ], [ 4561920, 1 ], [ 4809375, 1 ],
  [ 5103000, 2 ], [ 5332635, 1 ], [ 5878125, 1 ] ]