Yes it looks like calcite. The dark grey metallic-looking crystals maybe galena.
Thank you, I was thinking it to be quartz but could be calcite. Is it not quartz?
Oh, as another person mentioned. Looks like you have galena on the crystal. That is lead. A lead crystal.
Well galena is lead sulphide, PbS. It's the main ore of lead though.
The matrix is showing the typical calcite cleavage, which is the property of splitting preferentially in certain directions. With calcite, a sharp blow splits it into rhombohedrons, like the outline of your specimen. Quartz doesn't have any cleavage, and it's much harder (7 on Moh's scale).
Try a drop of vinegar on the creamy white areas. If it fizzes, you've got calcite.