Groups of order 64 are determined by their Tables of Marks

TL;DR

This paper proves that all groups of order 64 are uniquely identified by their Tables of Marks, resolving a question about groups of order less than 96.

Contribution

It establishes that groups of order 64 are uniquely determined by their Tables of Marks, answering a longstanding open question in group theory.

Findings

Groups of order 64 are uniquely determined by their Tables of Marks.

The result confirms that all groups of order less than 96 are determined by their Tables of Marks.

This work advances the classification of finite groups using combinatorial invariants.

Abstract

This paper shows that groups of order $64$ are uniquely determined up to isomorphism by their Tables of Marks. This then resolves a previously posed question about whether all groups of order less than $96$ are determined by their Tables of Marks.