I broke this coral in three pieces trying to fracture the rock it was on. More pics to come.
The little bit of the skeleton I can see reminds me of what you see growing under a candy cane coral. As if this mat of tissue is depositing a skeleton under itself, extending in an upward direction. There also seems to be "fingers" developing form a more central region of the mat.
Looking at pictures I have found on the other suggestions, Hydnopora looks the most like what I have.