20.109 (2022)

A skew brace is a set $B$ equipped with two operations $+$ and $\cdot$ such that $(B, +)$ is an additively written (but not necessarily abelian) group, $(B, \cdot)$ is a multiplicatively written group, and $a \cdot (b + c) = ab - a + ac$ for any $a, b, c \in B$.

Is there a finite skew brace with perfect additive group and non-perfect almost simple multiplicative group?