Let $S_n$ be the symmetric group of $n$ points. I want to find references (or proofs) for the following statement (1).

(1). There does not exist any faithful orthogonal representation $$ S_n\longrightarrow O(n-2). $$

In order to prove (1), I want to use the result that any unitary representation of $S_n$ is over $\mathbb{Q}$ and find references or proofs for the following statement (2).

(2). There does not exist any faithful unitary representation $$ S_n\longrightarrow U(n-2). $$

Where to find references for (1) or (2)?

Let $S_n$ be the symmetric group of $n$ points. I want to find references (or proofs) for the following statement (1).

(1). There does not exist any faithful orthogonal representation $$ S_n\longrightarrow O(n-2). $$

In order to prove (1), I want to use the result that any unitary representation of $S_n$ is over $\mathbb{Q}$ and find references or proofs for the following statement (2).

(2). There does not exist any faithful unitary representation $$ S_n\longrightarrow U(n-2). $$

Where to find references for (1)?

(if cannot, then find references for (2)? )