GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
# p1 = Z^2 # http://en.wikipedia.org/wiki/Wallpaper_group#Group_p1 M := [ [1,2,5], [1,2,7], [1,3,4], [1,3,9], [1,4,5], [1,7,9], [2,3,6], [2,3,8], [2,5,6], [2,7,8], [3,4,6], [3,8,9], [4,5,8], [4,6,7], [4,7,8], [5,6,9], [5,8,9], [6,7,9] ]; G := Group( () ); iso := rec(); mu := []; dim := 3; #matrix sizes: #[ 18, 108, 180, 135, 54, 9 ] #the torus # Z # Z^(1 x 2) # Z