Testing if an element is in the derived subgroup

Question

Let $ G $ be a finite group. Let $ G':=[G,G] $ be the derived subgroup. How do you test if an element $ g \in G $ is in $ G' $?

I'm specifically interested in how to do this in GAP. In other words I have a finite group $ G $ in GAP and I want to see if certain elements of $ G $ are in the derived subgroup $ G' $.

Is there a command for this like $ IsElement(G',g) $ or something?

For those who are interested in context, I'm looking at $ G $ the complex reflection group with Shephard-Todd number 31, and order 46080. In this case the derived subgroup $ G'=DerivedSubgroup(G) $ is index 2 and is isomorphic to $ PerfectGroup(23040,1) $.

Answer 1

The easiest would be g in DerivedSubgroup(G). In some cases (in particular finitely presented groups) going via the quotient is easier:

ma:=MaximalAbelianQuotient(G);
IsOne(Image(ma,g));