Linear representation theory of trivial group

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

Summary

Item	Value
degrees of irreducible representations over a splitting field	1 maximum: 1, lcm: 1, number: 1, sum of squares: 1
Schur index values of irreducible representations	1
condition for a field to be a splitting field	any field
smallest ring of realization of irreducible representations (characteristic zero)	$\mathbb {Z}$ -- ring of integers
smallest field of realization of irreducible representations (characteristic zero)	$\mathbb {Q}$

Character table

The character table for characteristic zero is:

Rep/Conj class	$e$ (identity element)
Trivial representation	1

There is a canonical bijection between the conjugacy classes and the irreducible representations here (unlike for bigger, more complicated groups). Indeed, it is the only bijection possible.