Conjugacy class size statistics need not determine degrees of irreducible representations

From Groupprops
Revision as of 02:03, 6 June 2011 by Vipul (talk | contribs) (Created page with "==Statement== It is possible to have two finite groups <math>G_1</math> and <math>G_2</math> such that the [[fact about::conjugacy class size statistics of a finite group|co...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search


It is possible to have two finite groups G_1 and G_2 such that the conjugacy class size statistics of G_1 are the same as those of G_2 (i.e., the two groups have the same number of conjugacy classes of each size) but the Degrees of irreducible representations (?) over \mathbb{C} for G_1 are not the same as those of G_2.


Further information: Linear representation theory of groups of order 128#Degrees of irreducible representations, element structure of groups of order 128#Conjugacy class sizes

The smallest examples are among groups of order 128.