GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
# S1 of p3m1
# http://en.wikipedia.org/wiki/Wallpaper_group#Group_p3m1
M := [ [1,2], [1,3], [2,5], [3,7], [5,6], [6,7] ];
S3 := Group( (1,2,3), (1,2) );
iso := rec( 1 := S3, 5 := S3, 7 := S3,
2 := Group( (1,2) ), 3 := Group( (1,3) ), 6 := Group( (2,3) ) );
mu := [];
dim := 3;
#----------------------------------------------->>>> Z^(1 x 1)
#----------------------------------------------->>>> Z^(1 x 1)
#----------------------------------------------->>>> Z/< 2 >