Why is the Fischer group $Fi_{24}'$ called $Fi_{24}'$ instead of $Fi_{24}$?

Question

I know that there is a sporadic simple group called $Fi_{24}'$. Why is there a prime symbol for this one when it isn't there for $Fi_{22}$ and $Fi_{23}$?

Answer 1

For a group $G$, it is common to denote its commutator subgroup by $G'$, which is where the prime symbol comes from.

There are certain $3$-transposition groups denoted by $Fi_{22}$, $Fi_{23}$, and $Fi_{24}$. There is more information in wikipedia, as pointed out in a comment.

Here $Fi_{22}$, $Fi_{23}$ are simple. The group $Fi_{24}$ is not simple, but its commutator subgroup $Fi_{24}'$ is simple (and of index $2$ in $Fi_{24}$).