A recent paper [H. Kahl and G. Köhler, J. Math. Anal. Appl. 232, 312–331 (1999; Zbl 0924.11032)] gives a table of all eta products that are modular forms of weight 1 on the Fricke groups \(\Gamma^*(N)\) of levels \(1\leq N\leq 23\). This paper discusses the case \(N= 36\) because it gives a particularly rich supply of eta products. There are many Hecke series of weight 1 on \(\Gamma^*(36)\), and identities are given relating these to eta products.