Daily Simple Group

Find today's finite simple group in 6 guesses. Pick any group from the table to read about it, then guess.

Symmetry has atoms

A group is a collection of symmetries

A square has 8 symmetries: 4 rotations and 4 flips. Doing one after another always gives another symmetry, and that rule is what makes them a group. The number of symmetries, here 8, is the group's order.

Simple groups are the atoms

Most groups can be broken into smaller groups, the way 12 breaks into 2 × 2 × 3. The ones that cannot be broken are called simple. Every finite group is built out of simple groups.

The classification lists all of them

The Classification of Finite Simple Groups says every finite simple group belongs to one of 18 infinite families, or is one of 26 sporadic groups that fit no family. The proof took about 100 mathematicians five decades and tens of thousands of pages. Axiom has now checked the whole proof by machine, in Lean 4.

How to play

Each guess compares your group with the answer. You get 6 guesses, and a new puzzle starts at midnight.

Matches the answer. In a prime column, both orders are divisible by that prime, or neither is. A struck-through number means your guess's order is not divisible by it.

Close: the answer's order is within a factor of 10 of yours.

Does not match. An arrow on the order says whether the answer is bigger or smaller.

The last two columns are about the primes 5 and 7. There is no column for 2, because every simple group that is not cyclic has an even order (Feit and Thompson, 1963, in a 255-page proof). The order of such a group also has at least three different primes (Burnside, 1904).