Tag: Cameron

  • The monster prime graph

    Here’s a nice, symmetric, labeled graph: The prime numbers labelling the vertices are exactly the prime divisors of the order of the largest sporadic group: the monster group $\mathbb{M}$. \[ \# \mathbb{M} = 2^{46}.3^{20}.5^9.7^6.11^2.13^3.17.19.23.29.31.41.47.59.71 \] Looking (for example) at the character table of the monster you can check that there is an edge between two […]

  • Sylvester’s synthemes

    I was running a bachelor course on representations of finite groups and a master course on simple (mainly sporadic) groups until Corona closed us down. Perhaps these blog-posts can be useful to some. A curious fact, with ripple effect on Mathieu sporadic groups, is that the symmetric group $S_6$ has an automorphism $\phi$, different from…