It looks like Calcite. A drop of acid will tell you right away if its Calcite, vinegar as well but not as violent of a reaction but will fizz. Calcite will also be scratched by a knife or pin.
Pick a flat surface and see if a piece of quartz or even a steel knife will scratch it easily, kind of looks like calcite I've collected before but that's just a guess, calcite has a hardness of 3 so both will scratch easily if its calcite, also acid test like fuss says....
If you want to clean it I'd just soak it in purified water, maybe use a little soap that doesn't have any acids in it like most antibacterial soaps have and use a brush with soft bristles to try and clean out the dirt in the crevices, I've ruined a lot of calcite specimens trying new ways of cleaning, even SIO hasn't worked well with the calcite specimens I've collected so now it's just hot water and soft bristles for me...