We show that in the complex reflection group G6, reflection factorizations of a Coxeter element that have the same length and multiset of conjugacy classes are in the same Hurwitz orbit. This confirms one case of a conjecture of Lewis and Reiner.
Gawankar, Gaurav; Lazreq, Dounia; Rai, Mehr; and Sabar, Seth
"Hurwitz Actions on Reflection Factorizations in Complex Reflection Group G₆,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 22:
2, Article 6.
Available at: https://scholar.rose-hulman.edu/rhumj/vol22/iss2/6