Sergei Ivanych is the principal of Moscow Elementary School #37. Check out the illustration of this guy at 23.F1. To put it bluntly, he looks like a three-fingered Hitler in a business suit. What we get from this character is a good impression of the cold brutality and unkindness of the Soviet political system. In particular, he helps us understand how Soviet children were treated in Yelchin's USSR, which is to say, terribly. He's also totes on the bandwagon of spouting off the over-the-top Communist propaganda: he thinks that whoever chipped the nose off of the statue is tantamount to a murderer.
He's short in stature (Sasha is surprised to discover), but tall on political purity. He gets way mad at Sasha for not coming to him and telling him that his dad has been arrested: "Had you done that [...] I would have let you denounce your father at today's Pioneers rally. Who knows, maybe we'd even let you join the Pioneers. But no, you chose to pretend that you are still one of us" (23.13).
There's a brief moment where Sergei Ivanych seems like he might have one kind bone in his body: "[He] sighs, sits back, and looks at us not unkindly" (23.18). But don't let this moment fool you. Right on the heels of that, he has zero problem sending Sasha and Vovka to the orphanage (23.18), and a bit later, he coldly shrugs off Finkelstein's parents being executed (27.7).
Oof, that's harsh. But remember, Sergei's one of many. Almost every adult in this novel is awful in one way or another.