Idealist running military group (7)

I believe the answer is:

platoon

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'military group' is the definition.
(I've seen this before)

'idealist running' is the wordplay.
'idealist' becomes 'plato' (I can't explain this - if you can you should give a lot more credence to this answer).
'running' becomes 'on' (eg when a machine is running it is on).
'plato'+'on'='PLATOON'

Can you help me to learn more?

(Other definitions for platoon that I've seen before include "Army unit" , "Soldiers under lieutenant" , "Division of company" , "Small military unit" , "Sub-unit of a military company" .)

I've seen this clue in The Guardian.

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