Linear representation theory of alternating group:A10: Difference between revisions
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==Summary== | |||
<section begin="summary"/> | |||
{| class="sortable" border="1" | |||
! Item !! Value | |||
|- | |||
| [[degrees of irreducible representations]] over a [[splitting field]] (such as <math>\overline{\mathbb{Q}}</math> or <math>\mathbb{C}</math>) || 1, 9, 35, 36, 42, 75, 84, 90, 126, 160, 210, 224, 224, 225, 252, 288, 300, 315, 350, 384, 384, 450, 525, 567<br>grouped form (by default each occurs once): 1, 9, 35, 36, 42, 75, 84, 90, 126, 160, 210, 224 (2 times) 225, 252, 288, 300, 315, 350, 384 (2 times), 450, 525, 567<br>[[maximum degree of irreducible representation|maximum]] 567, [[number of irreducible representations equals number of conjugacy classes|number]]: 24, [[sum of squares of degrees of irreducible representations equals order of group|sum of squares]]: 1814400 | |||
|} | |||
==GAP implementation== | |||
===Degrees of irreducible representations=== | |||
These can be computed using the [[GAP:CharacterDegrees|CharacterDegrees]] function: | |||
<pre>gap> CharacterDegrees(CharacterTable(AlternatingGroup(10))); | |||
[ [ 1, 1 ], [ 9, 1 ], [ 35, 1 ], [ 36, 1 ], [ 42, 1 ], [ 75, 1 ], [ 84, 1 ], [ 90, 1 ], [ 126, 1 ], [ 160, 1 ], [ 210, 1 ], [ 224, 2 ], [ 225, 1 ], | |||
[ 252, 1 ], [ 288, 1 ], [ 300, 1 ], [ 315, 1 ], [ 350, 1 ], [ 384, 2 ], [ 450, 1 ], [ 525, 1 ], [ 567, 1 ] ]</pre> | |||
Revision as of 00:58, 19 April 2012
This article gives specific information, namely, linear representation theory, about a particular group, namely: alternating group:A10.
View linear representation theory of particular groups | View other specific information about alternating group:A10
Summary
| Item | Value |
|---|---|
| degrees of irreducible representations over a splitting field (such as or ) | 1, 9, 35, 36, 42, 75, 84, 90, 126, 160, 210, 224, 224, 225, 252, 288, 300, 315, 350, 384, 384, 450, 525, 567 grouped form (by default each occurs once): 1, 9, 35, 36, 42, 75, 84, 90, 126, 160, 210, 224 (2 times) 225, 252, 288, 300, 315, 350, 384 (2 times), 450, 525, 567 maximum 567, number: 24, sum of squares: 1814400 |
GAP implementation
Degrees of irreducible representations
These can be computed using the CharacterDegrees function:
gap> CharacterDegrees(CharacterTable(AlternatingGroup(10))); [ [ 1, 1 ], [ 9, 1 ], [ 35, 1 ], [ 36, 1 ], [ 42, 1 ], [ 75, 1 ], [ 84, 1 ], [ 90, 1 ], [ 126, 1 ], [ 160, 1 ], [ 210, 1 ], [ 224, 2 ], [ 225, 1 ], [ 252, 1 ], [ 288, 1 ], [ 300, 1 ], [ 315, 1 ], [ 350, 1 ], [ 384, 2 ], [ 450, 1 ], [ 525, 1 ], [ 567, 1 ] ]