Taputimme yhdessä viimeisen laulun jälkeen.

Taputimme is the past tense, 1st person plural form of taputtaa.

Breakdown:

• taputtaa = to clap / to applaud
• taputimme = we clapped / we applauded

So the ending -imme tells you the subject is we, and the past-tense marker is part of the verb form.

It can mean both, depending on context.

In this sentence, taputimme most naturally means we applauded or we clapped after a performance.

So:

• taputtaa = to clap one’s hands
• in performance contexts, it often means to applaud

After the last song, the intended meaning is clearly applause.

Because they belong to the phrase viimeisen laulun jälkeen = after the last song, and jälkeen is a postposition that requires the noun phrase before it to be in the genitive.

So:

• viimeinen = last
• viimeisen = of the last / last (genitive form)
• laulu = song
• laulun = of the song / song (genitive form)

Also, the adjective agrees with the noun:

• viimeinen laulu = the last song
• viimeisen laulun = of the last song / the last song in genitive

Because jälkeen is a postposition, not a preposition.

In English, we say:

• after the last song

In Finnish, the equivalent structure is:

• the last song + after
• viimeisen laulun jälkeen

This is very common in Finnish. Some words that correspond to English prepositions actually come after the noun phrase.

Yhdessä means together.

It is an adverb, so it describes how the action happened:

• Taputimme yhdessä = We clapped together

It does not change its form here, and it does not need to agree with anything else in the sentence.

Because Finnish can use taputtaa without an object when the meaning is simply to clap or to applaud.

So:

• Taputimme. = We clapped.
• Taputimme yhdessä. = We clapped together.

You do not need to add a word like hands. Finnish often leaves that unstated when it is obvious from the verb.

No, Finnish word order is fairly flexible.

This sentence has a natural, neutral order:

• Taputimme yhdessä viimeisen laulun jälkeen.

But other orders are also possible, for example:

• Viimeisen laulun jälkeen taputimme yhdessä.
• Yhdessä taputimme viimeisen laulun jälkeen.

The basic meaning stays the same, but the emphasis can shift:

• putting viimeisen laulun jälkeen first emphasizes the time
• putting yhdessä earlier can emphasize together

Yes. In many contexts, viimeinen laulu can be translated as either the last song or the final song.

The Finnish word viimeinen covers both ideas. Which English version sounds best depends on context:

• after the last song = very direct translation
• after the final song = often more natural in a concert or performance setting

Here are the dictionary forms:

• Taputimme → taputtaa = to clap, to applaud
• yhdessä → yhdessä = together
• viimeisen → viimeinen = last, final
• laulun → laulu = song
• jälkeen → jälkeen = after

So the sentence is built from very common Finnish words and one common postposition structure.

This is standard written Finnish.

In everyday spoken Finnish, people often use different forms, especially for we forms. But taputimme yhdessä viimeisen laulun jälkeen is perfectly normal and correct standard Finnish.

For a learner, this is the right form to study first.