A group with three real irreducible characters: answering a question of Moreto and Navarro

TL;DR

This paper constructs a specific group with three real irreducible characters, addressing a question about the existence of such groups with particular Sylow 2-subgroup structures.

Contribution

It provides a concrete example of a group with three real irreducible characters and a Sylow 2-subgroup as an iterated central extension of a Suzuki 2-group, answering an open question.

Findings

Constructed a group with three real irreducible characters

Sylow 2-subgroup is an iterated central extension of a Suzuki 2-group

Addresses an open question by Moreto and Navarro

Abstract

In this paper, we construct a group with three real irreducible characters whose Sylow 2-subgroup is an iterated central extension of a Suzuki 2-group. This answers a question raised by Moreto and Navarro who asked whether such a group exists.