# 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…