A New Maximal Subgroup of the Monster

The Character Table of a Maximal Subgroup of the Monster

We calculate the character table of the maximal subgroup of the Monster N(3B) ∼= 3 + .2.Suz:2, and also of the group 31+12:6.Suz:2, which has the former as a quotient. The strategy is to induce characters from the inertia groups in 31+12:6.Suz:2 of characters of 3. We obtain the quotient map to N(3B) computationally, and our careful concrete approach allows us to produce class fusions between o...

On the Fischer-Clifford matrices of a maximal subgroup of the Lyons group Ly

The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...

A correction to the 41-structure of the Monster, a construction of a new maximal subgroup L2(41) and a new Moonshine phenomenon

We correct the result of a previous paper which purported to show that L2(41) was not a subgroup of M. Our main result is that there is exactly one conjugacy class of subgroups L2(41) in the Monster. Such subgroups are self-normalizing and maximal. This leads to a new unexplained Moonshine phenomenon.

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

Explicit representations of maximal subgroups of the Monster

Most of the maximal subgroups of the Monster are now known, but in many cases they are hard to calculate in. We produce explicit ‘small’ representations of all the maximal subgroups which are not 2-local. The representations we construct are available on the World Wide Web at http://brauer.maths.qmul.ac.uk/Atlas/. 1 The maximal subgroups of the Monster By the work of several authors [13, 14, 17...