Group $A_5$ has presentation $〈 a, b | a^2 = b^3 = (ab)^5 = 1 〉$. Items equal to 1 are **relators**, so a presentation of $A_5$ as a set of relators could be
$(a^2, b^3, (ab)^5)$

$Q_{16}$ is SmallGroup(16,9) with $〈 a, b | a^4 = b^2 = abab 〉$.

In GAP, $A_5$ is SmallGroup(60,5). The following code:

RelatorsOfFpGroup(Image(IsomorphismFpGroup(SmallGroup(60,5))));

will give

[ F1^5*F2^-5, F1^5*F2^-1*F1^-1*F2^-1*F1^-1, F1^-2*F2^2*F1^-2*F2^2 ]

That's not what I'm looking for. How can I get GAP to give me a presentation, or a minimal set of relators? Is there a single line piece of code that will work for most SmallGroup items?

thepresentation of a finitely presented group. GAP cannot read your mind and determine which one you want, exactly. And even if it could, then the unfortunate fact is that many problems related to finite presentation are generally algorithmically unsolvable. Such as deciding whether two given finite presentations describe isomorphic groups. – Max Horn Dec 22 '11 at 23:16