Geodesic
WEAK CAYLEY TABLE GROUPS OF SOME CRYSTALLOGRAPHIC GROUPS
Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 635-660

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DOI

For a group G, a weak Cayley table isomorphism is a bijection f : G → G such that f(g1g2) is conjugate to f(g1)f(g2) for all g1, g2 ∈ G. The set of all weak Cayley table isomorphisms forms a group (G) that is the group of symmetries of the weak Cayley table of G. We determine (G) for each of the 17 wallpaper groups G, and for some other crystallographic groups. 
HUMPHRIES, STEPHEN P.; PAULSEN, REBECA A. WEAK CAYLEY TABLE GROUPS OF SOME CRYSTALLOGRAPHIC GROUPS. Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 635-660. doi: 10.1017/S0017089517000337
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     author = {HUMPHRIES, STEPHEN P. and PAULSEN, REBECA A.},
     title = {WEAK {CAYLEY} {TABLE} {GROUPS} {OF} {SOME} {CRYSTALLOGRAPHIC} {GROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {635--660},
     year = {2018},
     volume = {60},
     number = {3},
     doi = {10.1017/S0017089517000337},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000337/}
}
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