This is the 7784th most frequent Russian word.
инсарскому
The word "инсарскому" is a dative singular form of the adjective "инсарский," meaning "related to Insar," a town in Russia.
The word 'инсарскому' is used as an adjective referring to something related to Insarsk (a toponym), agreeing with 'отделу' in dative case.
Я передал все документы инсарскому отделу.
I handed all the documents to the Insarsky department.
Here, 'инсарскому' modifies 'народу', indicating the people associated with Insarsk, again in dative case.
Новые правила были инсарскому народу на пользу.
The new rules were beneficial to the Insarsk people.
In this instance, 'инсарскому' describes the union related to Insarsk, matching 'союзу' in dative following the verb 'дал'.