The character table of a split extension of the Heisenberg group $H_1(q)$ by $Sp(2,q)$, $q$ odd

TL;DR

This paper computes the complete character table of a split extension of the Heisenberg group by the symplectic group over a finite field of odd characteristic, advancing understanding of their representation theory.

Contribution

It provides the first explicit determination of the full character table for this specific split extension, linking the Heisenberg and symplectic groups.

Findings

Complete character table of the split extension is obtained.

New insights into the representation theory of Heisenberg and symplectic groups.

Facilitates further algebraic and combinatorial applications.

Abstract

In this paper we determine the full character table of a certain split extension $H_1(q)\rtimes Sp(2,q)$ of the Heisenberg group $H_1$ by the odd-characteristic symplectic group $Sp(2,q)$.