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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) by the "spider relation": (ab1c1d1ab2c2d2ab3c3d3)^10. In this presentation, a is the generator in the center of the coxeter diagram, and bi, ci, di is the first three generators on a spoke (for i ranging from 1 to 3).

I was experimenting with the smaller group Y222, and I found that it had order 12597120 = 2^7*3^9*5. Unfortunately, Magma was unable to find the composition factors of G. What are the composition factors?

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  • $\begingroup$ This paper - ftp.mathe2.uni-bayreuth.de/axel/papers/ivanov:the_monster.ps.gz - seems to assert that ${Y222}\cong 3^5. O_5(3)$. By the way, your questions would be much easier to read if you used LaTeX! $\endgroup$
    – Nick Gill
    Mar 11, 2015 at 8:59
  • $\begingroup$ According to page 233 of the ATLAS, it is $3^5:O_5(3):2$. If you want help with a Magma or GAP computation, then please write down the presentation. $\endgroup$
    – Derek Holt
    Mar 11, 2015 at 9:01
  • $\begingroup$ That's interesting - there seems to be a discrepancy there. But $3^5: O_5(3):2$ does have order $12597120$. $\endgroup$
    – Derek Holt
    Mar 11, 2015 at 9:05
  • $\begingroup$ Should be easy to check, I suppose. $\endgroup$
    – Dima Pasechnik
    Mar 11, 2015 at 9:22

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