G:=Group(
(1,2,4,6,8)(3,5,7,9,10)(11,12,13,15,17)(14,16,18,20,22)(19,21,24,27,29)(23,26,
28,30,25),
(1,3)(10,11)(12,14)(17,19)(20,23)(21,25)(24,28)(29,31));
m2 := [
[[0,1,0,0,0],
[0,0,1,0,0],
[0,0,0,1,0],
[0,0,0,0,1],
[1,0,0,0,0]],

[[1,1,0,0,0],
[0,1,0,0,0],
[0,0,1,0,0],
[0,0,0,1,0],
[0,0,0,0,1]]]*Z(2);

iso:=IsomorphismFpGroup(G);
F:=Image(iso);