In the paper:

Kac, Victor; Watanabe, Keiichi, *Finite linear groups whose ring of invariants is a complete intersection.* Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 2, 221–223

it is said in Remark 2 on page 222 that for any finite subgroup $G$ of $GL_2(\mathbb{C})$ the ring of invariants $\mathbb{C}[X_1, X_2]^G$ is always a complete intersection ring without any reference.

Can anyone kindly tell me a reference for this result? Thank you.