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The Monster group (actually the bimonster) has a presentation as Y555. Y555 is the quotient of a coxeter group (the coxeter diagram is a central node with three "spokes" coming out of it with length 5 …

In the question "Simple Hurwitz Groups of order less than 10^7", it came up that all the Hurwitz groups with absolutely irreducible projective representations of degrees up to 7 over any field are det …

It was shown that the only quotient of the group $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^{10} \rangle$ of the form PSL(2, q) is PSL(2, 41). That lead me to consider other families of simple g …

Conjecture: Let $p$ be a prime. Then the group $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^9, (([a,b]^4)b)^{2p} \rangle$ has a composition series of the form ${\rm PSL}(2,8) - {\rm Z}_p - {\r …

Since my question at Simplicity of infinite groups was not answered (well, at least, my second question), instead of trying to find the isomorhism type of those groups, I will instead try to find the …

I was experimenting with various presentations for groups, and I stumbled upon $G := \langle a, b \ | \ a^2, b^3, (ab)^7, [aba,b]^6 \rangle$. I found that it has order 11741184, but the magma calculat …

Actually, I just figured it out. The groups $H := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^{28}, [aba,b]^6 \rangle$ and $I := \langle a, b \ | \ a^2, b^3, (ab)^7, [a,b]^{8}, [aba,b]^6 \rangle$ are …

How many times is each alternating group a hurwitz quotient? In other words, how many non-isomorphic ways can an alternating group be generated by an element of order 2 and an element of order 3 whose …

I'm trying to calculate a table of all simple hurwitz groups of order less than 10^7. None of the tables I found went further than 10^6, so I decided to use the tables of all simple groups up to 10^7 …

The Monster group is the largest of the sporadic simple groups, and has been proven by Wilson to also be a Hurwitz group. It has a presentation in terms of Coxeter groups, specifically Y443 along with …

I was reading about the monster group, and how hard it was to do calculations in it, and I wondered: Is there a known presentation of the monster group? I know that it is a hurwitz group, but other th …

The gnu (or Group NUmber) function describes how many groups there are of a given order. The number of groups of each order are known up to 2047, see https://www.math.auckland.ac.nz/~obrien/research/g …