Let $G=H\times T$ such that $H$ is 2-generated p-group of class two and $H$ be abelian p- group. We know if $H$ and $T$ are capable groups, then $G$ is capable. 


**Question:** Is the converse correct or no? i.e 


If $G$ is a capable group then are $T$ or $H$( both $H$ and $T$) capable? 



On direct product of capable groups
Let $H$ be extraspecial of order $p^3$ and exponent $p$ (for odd $p$), and $T=C\_p$. Then $G=H \times T$ is capable but $T$ is not.


We have $G = K/Z(K)$, where 
$$K= \langle a,b,c,d,e,f \mid [a,b]=c,[a,c]=e,[b,c]=f, [a,d]=e,
[b,d]=[c,d]=1,$$ $$a^p=b^p=d^p=1, e,f {\rm\ central} \rangle.$$


