# An exotic presentation of Q_28

## TL;DR

This paper introduces a novel family of presentations for quaternion groups, demonstrating that for the order 28 quaternion group, a specific presentation exhibits a non-standard second homotopy group, revealing new algebraic properties.

## Contribution

It presents a new family of presentations for quaternion groups and identifies a unique case with non-standard second homotopy group for order 28.

## Key findings

- New presentations for quaternion groups introduced
- Order 28 quaternion group has a non-standard second homotopy group in one presentation
- Provides insights into algebraic topology of quaternion groups

## Abstract

We introduce a new family of presentations for the quaternion groups and show that for the quaternion group of order 28, one of these presentations has non-standard second homotopy group.