Listing the elements of a symmetry group of a frieze pattern

[JohnMcBetty]

I have run into a problem where I have a frieze pattern F, the frieze pattern has horizontal refelctive symmetry, glide reflective symmetry, but does not have 180 degree rotation and does not have vertical reflective symmetry.

G represents the symmetry group for F. G={reflection symmetry, translational symmetry} and the mirror of the reflection is parallel to the vector of the translation. Hence a glide reflection with the translation composed with the reflection.

I now have to list the elements of G, not exactly sure what to do at that point. Can anybody help me out?

 

[Deveno]

this sounds like the "jump" frieze group, which is isomorphic to Z x Z2, and generated by
the horizontal translation (1,0) and the horizontal reflection (0,1). a glide reflection is of the form (k,1). as with any frieze group it is infinite, but we have basically 4 types of symmetries:

(k,0), a translation
(k,1), a glide reflection
(0,1), the horizontal reflection
(0,0), the identity.