Is there a table showing Sporadic Groups and their exponents, and, perhaps, other basic properties. In particular, I'm interested in what the exponent of the Monster Group is. (Obviously the order is well publicised, but not the exponent, as far as I can tell.) Thanks!

From the comments, This information can be calculated easily from the printed character tables in the ATLAS of Finite Groups (which include orders of elements in conjugacy classes) or, perhaps more conveniently, using the same information online via GAP or Magma. From there you can just load the character table from the library and calculate the lcm of the orders of the elements. I had a quick look at the character table of the Monster in the Atlas, and its exponent appears to be 32.27.25.7.11.13.17.19.23.29.31.47.59.71.41 - Derek Holt

Or, using the version of the ATLAS tables in Gap's character table library, Exponent(CharacterTable("F1")); (returns 1165654792878376600800) for the exponent of the Monster. – Gro-Tsen

`Exponent(CharacterTable("F1"));`

(returns`1165654792878376600800`

) for the exponent of the Monster. $\endgroup$ – Gro-Tsen Feb 10 '20 at 11:32