Let $G$ be a finite group. Let $p$ be a prime dividing $|G|$. Let $k:=\overline{\mathbb{F}_p}$.

Let $b$ be a $p$-block of $kG$ with abelian defect group $D$. Let $H:=N_G(D)$. Let $c$ be the Brauer correspondent of $b$.

M. Broué conjectured in the 90's that $b$ and $c$ are derived equivalent under these assumptions.

I would like to ask the following:

Questions:

1. Does there exist a recent list of small groups for which this conjecture has been verified?
2. E.g., is it true for all small groups of order less than $200$, say ?
3. What is the smallest example (w.r.t. $|G|$) which is not yet verified?

Thank you very much for the help.

Let $G$ be a finite group. Let $p$ be a prime dividing $|G|$. Let $k:=\overline{\mathbb{F}_p}$.

Let $b$ be a $p$-block of $kG$ with abelian defect group $D$. Let $H:=N_G(D)$. Let $c$ be the Brauer correspondent of $b$.

M. Broué conjectured in the 90's that $b$ and $c$ are derived equivalent under these assumptions.

I would like to ask the following:

Questions:

1. Does there exist an up-to-date list of small groups for which this conjecture has been verified?
2. E.g., is it true for all small groups of order less than $200$, say ?
3. What is the smallest example (w.r.t. $|G|$) which is not yet verified?

Thank you very much for the help.