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We study the class 
$\operatorname {Erg}^\perp $ of automorphisms which are disjoint with all ergodic systems. We prove that the identities are the only multipliers of 
$\operatorname {Erg}^\perp ,$ that is, each automorphism whose every joining with an element of 
$\operatorname {Erg}^{\perp }$ yields a system which is again an element of 
$\operatorname {Erg}^{\perp }$, must be an identity. Despite this fact, we show that 
$\operatorname {Erg}^\perp $ is closed by taking Cartesian products. Finally, we prove that there are non-identity elements in 
$\operatorname {Erg}^\perp $ whose self-joinings always yield elements in 
$\operatorname {Erg}^\perp $. This shows that there are non-trivial characteristic classes included in 
$\operatorname {Erg}^\perp $.
