Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-12T12:26:58.732Z Has data issue: false hasContentIssue false

35 - The 3-modular characters of the McLaughlin group McL and its automorphism group McL.2

Published online by Cambridge University Press:  07 September 2010

Get access

Summary

Introduction

McLaughlin's sporadic simple group McL was originally constructed (see) as a permutation group on 275 letters. It is a simple group of order 898128000 = 27.36.53.7.11. It is now known to be the pointwise stabilizer of a 2-dimensional sublattice in the Leech lattice. Its maximal subgroups were found by Finkelstein (see). The modular character tables for the relevant primes p = 2, 7 and 11 were found by Thackray. The 5-modular character tables were found by Hiss, Lux and Parker, up to a few ambiguities (see). These ambiguities together with others in the values of the 5- modular characters 560 and 3038 of the automorphism group of McL, denoted by McL.2, were resolved by Suleiman (see). The main purpose of this paper is to complete the 3-modular character table of McL and to find the 3-modular character table of McL.2.

The 3-modular character table of McL

In this section we are going to complete what has been done by R. Parker on the 3-modular characters of McL. To do so we have to work out again most of the 3-modular characters using the techniques of the ‘Meat-Axe’ which is the main tool in our work. We then use the method of ‘condensation’ (see) to complete the 3-modular character table of McL.

The central characters modulo 3 give the block distribution of the ordinary irreducible characters. There are three blocks of defect zero. These blocks are B1 = {5103}, B2 = {8019a} and B3 = {8019b}. Hence, 5103, 8019a and 8019b are three 3-modular irreducible characters in McL.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×