Dear GAP - Forum,

Last week Joachim Neubueser sent a collection of
exercises for the use of GAP with courses in Algebra and
Group Theory.
In one of the exercises it is claimed that

G := <(2,3,5,6,8,12)(7,10,9,14,11,13),(1,2,4)(5,7,11)(6,9,10)(8,13,14)>

is isomorphic to SL(2,13).

In fact, G is isomorphic to PSL(2,13).

gap> G :=
Group((2,3,5,6,8,12)(7,10,9,14,11,13),(1,2,4)(5,7,11)(6,9,10)(8,13,14));;

gap> Size(G);
1092
gap> IsSimple(G);
true
gap> SL2_13 := SpecialLinearGroup(2,13);;
gap> Size(SL2_13);
2184                                  # |SL(2,13)| = ((13^2 - 1)(13^2 -
13))/12 = 2|G|

Best regards,

Stefan Kohl