Essential Dimension of Small Finite Groups

TL;DR

This paper calculates the essential dimension, a measure of complexity, for all small finite groups with order up to 63, providing a comprehensive understanding of their algebraic properties.

Contribution

It offers the first complete computation of the essential dimension for all finite groups of order up to 63, filling a gap in the existing literature.

Findings

Essential dimension values for groups of order ≤ 63 are determined.

Provides a complete classification of essential dimensions for small finite groups.

Enhances understanding of algebraic complexity in finite group theory.

Abstract

We compute the essential dimension of finite groups of order $\leqslant 63$.