Projective (or spin) representations of finite groups. II

TL;DR

This paper extends the classification and character computation of irreducible projective (spin) representations of finite groups, focusing on cases where the Schur multiplier contains the prime 3, building on previous work with prime 2.

Contribution

It provides a complete list of irreducible spin representations and their characters for finite groups with Schur multiplier involving prime 3, expanding prior classifications.

Findings

Classified irreducible spin representations based on their spin types.

Computed spin characters for these representations.

Extended the analysis from prime 2 to prime 3 cases.

Abstract

In the previous paper, we proposed a practical method of constructing explicitly representation groups $R(G)$ for finite groups $G$, and apply it to certain typical finite groups $G$ with Schur multiplier $M(G)$ containing prime number 3. In this paper, we construct a complete list of irreducible projective (or spin) representations of $G$ and compute their characters (called spin characters). It is a continuation of our study of spin representations in the cases where $M(G)$ contains prime number 2 to the cases where other prime $p$ appears, firstly $p=3$. We classify irreducible spin representations and calculate spin characters according to their spin types.