The Monster Group & Finite Groups – John Conway
Familiar with the Atlas of Finite Groups by John Conway? This book gives a complete descriptions of all the finite simple groups.
The first 15 pages is a brief overview of the simple finite groups of various types and how they are defined. The next 15 pages is an explanation of the machine-code-like databases that follow on so many finite groups. So far we are still in the preamble.
The meat of the book (the next 200 pages) is a vast database on about 90 of the more unique or important finite simple groups, including all of the sporadic groups. This includes (among many other things) the character tables for the groups — which can be quite large. The Monster’s character table is 194×194 matrix of values — some of the values are 10+ digit numbers — this takes a about 8 pages of tiny type on this massive book.
This was a remarkable and important book when it was written. Today, I think it is still useful as a reference, but for experts this kind of information is now more easily stored and transferred in digital libraries.
The Monster Group explained
Periodic Table of Groups explained
Life, Death and The Monster Group