Coal ash consists primarily of oxides of silicon, aluminum, iron, and calcium.
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But it is not rock. QED. Its compressed vegetable matter.
1) Coal is a sedimentary rock.
2) Coal ASH has had all the carbon burned out of it, and has been melted and cooled. It would constitute a sort of synthetic metamorphic rock
I’m not clear on where you studied geology, but it seems to have been deficient.