Are Channel Divinity powers not usable in antimagic fields?
As per a Jeremy Crawford tweet:
Channel Divinity creates magical effects (stated in both the cleric and the paladin). [...]
From the PHB:
At 2nd level, you gain the ability to channel divine energy directly from your deity, using that energy to fuel magical effects.
So they would not work inside an antimagic field which states:
Spells and other magical effects, except those created by an artifact or a deity, are suppressed in the sphere and can't protrude into it.