Really great performance — furious father’s left (8)

I believe the answer is:

gigantic

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'really great' is the definition.
'gigantic' can be an answer for 'great' (I've seen this before). I am not certain of the 'really' bit.

'performance furious father's left' is the wordplay.
'performance' becomes 'gig' (I've seen this before).
'furious father's left' becomes 'antic' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'gig'+'antic'='GIGANTIC'

Can you help me to learn more?

(Other definitions for gigantic that I've seen before include "Hugh,colossal" , "monster" , "Great big" , "Fantastically great" , "'Enormous, mammoth (8)'" .)

I've seen this clue in The Times.

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