# G=(16, 13) notation

I hope this is an easy question but no so easy to be wiped out. I have asked few physical people (Profs) here in our department, and nobody has a clue. I'm reading this paper:

The locus of curves with prescribed automorphism group

and it uses following notation to represent a group:

G = (16, 13)

This is at the beginning of page 11. Shaska uses this notation in his other papers but I couldn't find an explanation for the kind of groups he's talking about. Could you please tell me exactly what's the meaning of this bracket notation? It could be a GAP thing but unfortunately I'm not a GAP person.

Thanks a lot.

• This seems to refer to the number of the finite group in the GAP database. The first number is the order of the group and the second is the GAP-specific number of that particular group among all groups of that order. E.g. in MAGMA, this group is created with the command SmallGroup(16,13). – Alex B. Feb 22 '11 at 6:38
• I see. So it's the 13th group of order 16. Is GAP using a particular way to order all groups of order n? – André Henriques Feb 22 '11 at 10:23
• Not a GAP person, yet. – Kevin O'Bryant Feb 22 '11 at 15:50

If Alex Bartel is correct that the notation $(16,13)$ refers to SmallGroup(16,13), then here are generators for your group: $$\left\{\left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array} \right),\left( \begin{array}{cc} -i & 0 \\ 0 & i \end{array} \right),\left( \begin{array}{cc} 1 & 0 \\ 0 & -1 \end{array} \right)\right\}$$