Pagans had The Omen distributed (10)

I believe the answer is:

heathendom

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'pagans had the omen distributed' is the definition.
I can't judge whether this definition defines the answer.

'had the omen distributed' is the wordplay.
'distributed' indicates anagramming the letters.
'had'+'the'+'omen'='hadtheomen'
'hadtheomen' with letters rearranged gives 'HEATHENDOM'.

Can you help me to learn more?

(Other definitions for heathendom that I've seen before include "hellish circumstances" , "Uncivilised lot" , "damned foreigners" , "land outside the church" .)

I've seen this clue in The Times and The Sunday Times.

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