Linear representation theory of Conway group:Co0

This article gives specific information, namely, linear representation theory, about a particular group, namely: Conway group:Co0.
View linear representation theory of particular groups | View other specific information about Conway group:Co0

Summary

Item	Value
degrees of irreducible representations over a splitting field (such as $\bar{Q}$ or $C$ )	too long to list, see Linear representation theory of Conway group:Co0#GAP implementation number: 167, sum of squares: 8315553613086720000, maximum: 1021620600, quasirandom degree: 24

Irreducible representations

Smallest degree nontrivial irreducible representation

We know that the Conway group is the automorphism group of the Leech lattice. All automorphisms of a lattice are linear automorphisms, hence this action defines a linear representation of the Conway group $C_{o 0}$ on a 24-dimensional representation over the real numbers. This representation is irreducible over the complex numbers and is the smallest degree nontrivial irreducible representation.

Note that the representation is faithful, and it does not descend to an irreducible representation of Conway group:Co1.

Some information on its irreducible representations is, and we use the symbol "2.Co1" to access this information. The degrees of irreducible representations can be computed using the CharacterDegrees and CharacterTable functions.

gap> CharacterDegrees(CharacterTable("2.Co1"));
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