This is the 7364th most frequent Russian word.
гиагинском
"Гиагинском" is the prepositional case of "Гиагинский," referring to something related to Giaginskaya, a settlement in Russia.
Here, "Гиагинском" is used as the locative case form to refer to being in the location of Giaginsk.
Я был в Гиагинском на выходных.
I was in Giaginsk on the weekend.
In this sentence, "Гиагинском" again refers to the locative case, describing an event occurring in the Giaginsk district.
Обсуждение проекта началось в Гиагинском районе.
The discussion of the project began in the Giaginsk region.
Here, "Гиагинском" is used in a descriptive sense within a sentence to indicate the location being referred to.