TITLE: Finding Presentations of Groups with GAP
QUESTION [5 upvotes]: 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 $〈 a, b | a^4 = b^2 = abab 〉$.
More groups of size 16
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?

REPLY [7 votes]: I am not sure what exactly you are looking for (GAP IS giving you some presentation). However, if you are looking for a simpler presentation, check out this discussion:
http://mail.gap-system.org/pipermail/forum/2011/003313.html