Blew up school with unfashionable exterior (9)

I believe the answer is:

detonated

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'blew up' is the definition.
('detonate' can be a synonym of 'blow up')

'school with unfashionable exterior' is the wordplay.
'school with' becomes 'eton' (famous UK public school. I am not sure about the 'with' bit.).
'unfashionable' becomes 'dated' (similar in meaning).
'exterior' means one lot of letters goes inside another (some letters go on the outside of others).
'eton' put inside 'dated' is 'DETONATED'.

Can you help me to learn more?

(Other definitions for detonated that I've seen before include "let off" , "Blown up" , "Set off" .)

I've seen this clue in The Times.

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