This file comtains inf about the orders of some of the
products of the generators of the group G.

gap> group_r1:=Group(r1);
Group( (1,2,3,4,5,6,7,8) )
gap> Size(group_r1);
8
gap> group_r1xf1:=Group(r1*f1);
Group( ( 1,27, 2,26, 3,25, 4, 5, 6, 7, 8,28)( 9,20)(10,19)(11,18)(12,17) )
gap> Size(group_r1xf1);
12
gap> (r1*f1)^(12);
()
gap> group_f1xf2xf3:=Group(f1*f2*f3);
Group( ( 1,30, 3,28)( 2,29)( 4,25, 6,27)( 5,26)( 9,13,24,20)(10,14,19,12,17,
 23,21)(11,18) )
gap> Size(group_f1xf2xf3);
28
gap> group_f1xf2xf3xf4:=Group(f1*f2*f3*f4);
Group( ( 1, 5,26,30, 3, 7,28)( 2, 6,27,31, 4,25,29)( 9,22,13,24,15,20)(10,21)
(11,18)(12,17)(14,19,23) )
gap> Size(group_f1xf2xf3xf4);
42
gap> (f1*f2*f3*f4)^(42);
()
gap> group_[f1,f2]:=Group(f1*f2*f1*f2);
Syntax error: ] expected
group_[f1,f2]:=Group(f1*f2*f1*f2);
         ^
gap> group_[f1_f2]:=Group(f1*f2*f1*f2);
Error, Variable: 'group_' must have a value
gap> group_commf1f2:=Group(f1*f2*f1*f2);
Group( ( 1, 5,28, 3,26)( 2,25,29, 4,27)(10,21,19)(11,22,18)(12,23,17) )
gap> Size(group_commf1f2);
15
gap> group_commf1r1:=Group(f1*r1*f1*r1^(-1));
Group( ( 1, 8,28,27,26,25, 4, 3, 2) )
gap> Size(group_commf1r1);
9
gap> group_commf1f2f3:=Group(f1*f2*f3*f1*f2*f3);
Group( ( 1, 3)( 4, 6)( 9,24)(10,19,17,21,14,12,23)(13,20)(25,27)(28,30) )
gap> Size(group_commf1f2f3);
14
gap> 
gap> r1;f1;r1*f1;
(1,2,3,4,5,6,7,8)
( 1,28)( 2,27)( 3,26)( 4,25)( 9,20)(10,19)(11,18)(12,17)
( 1,27, 2,26, 3,25, 4, 5, 6, 7, 8,28)( 9,20)(10,19)(11,18)(12,17)
gap> f1;f2;f1*f2;
( 1,28)( 2,27)( 3,26)( 4,25)( 9,20)(10,19)(11,18)(12,17)
( 2,29)( 3,28)( 4,27)( 5,26)(10,21)(11,22)(12,23)(13,24)
( 1, 3, 5,26,28)( 2, 4,25,27,29)( 9,20)(10,19,21)(11,18,22)(12,17,23)(13,24)
gap> r1;r1^(-1);r1^2;r1^3;
(1,2,3,4,5,6,7,8)
(1,8,7,6,5,4,3,2)
(1,3,5,7)(2,4,6,8)
(1,4,7,2,5,8,3,6)
gap> f1;f2;f3;f4;f1*f2*f3*f4;
( 1,28)( 2,27)( 3,26)( 4,25)( 9,20)(10,19)(11,18)(12,17)
( 2,29)( 3,28)( 4,27)( 5,26)(10,21)(11,22)(12,23)(13,24)
( 3,30)( 4,29)( 5,28)( 6,27)(11,22)(12,21)(13,20)(14,19)
( 4,31)( 5,30)( 6,29)( 7,28)(12,23)(13,22)(14,21)(15,20)
( 1, 5,26,30, 3, 7,28)( 2, 6,27,31, 4,25,29)( 9,22,13,24,15,20)(10,21)(11,18)
(12,17)(14,19,23)
gap> quit;