This is the 8341st most frequent Russian word.
михайловском
"Mихайловском" refers to "Mikhaylovsky" in English, typically indicating something related to Mikhaylovsky, such as a place, institution, or possession.
In this sentence, 'михайловском' (Mikhailovsky) is used as an adjective to describe the park, specifying it as the one related to 'Mikhailovsky'.
Я недавно был в Михайловском парке.
I recently visited the Mikhailovsky park.
Here, 'михайловского' (Mikhailovsky) serves as an adjective in the genitive case to detail the palace from which the painting originates.
На выставке представлена картина из Михайловского дворца.
The exhibition features a painting from the Mikhailovsky palace.
In this usage, 'михайловском' (Mikhailovsky) qualifies the theater, indicating its name and/or related origin.