$3$-length of $(C_3\times C_3):GL(2,3)$ in GAP

Question

I try to find $3$-length of the semidirect products group $(C_3\times C_3):GL(2,3)$. $p$-length means the number of factors in the shortest subnormal series which factors are $p$-groups or $p'$-groups. I can not find a command in GAP. I guess it's $4$ by its composition series.

Answer 1

${\rm GL}(2,3)$ has the structure $Q_8:S_3 = Q_8:(3:2)$, so yes, the $p$-length is $4$.

To compute the $p$-length of a $p$-solvable group $G$ in GAP, first compute $O_{p'}(G)$, then $O_{p'p}(G)$, which is the inverse image of $O_p(G/O_{p'}(G))$, then $O_{p'pp'}(G)$, and carry on until you reach $G$.