On the classification of quandles of low order

TL;DR

This paper classifies all indecomposable quandles of size less than 36 using transitive group classification, providing a comprehensive list and implementing it in the Rig GAP package for further algebraic computations.

Contribution

It offers the first complete classification of small indecomposable quandles and integrates this into the Rig GAP package, facilitating future algebraic research.

Findings

Complete list of indecomposable quandles under 36 elements.

Identification of quandles not of type D within this size range.

Implementation of classification results in the Rig GAP package.

Abstract

Using the classification of transitive groups we classify indecomposable quandles of size <36. This classification is available in Rig, a GAP package for computations related to racks and quandles. As an application, the list of all indecomposable quandles of size <36 not of type D is computed.