The DF12C-36DS-0.5V(81): This is a Hirose DF12 series board-to-board receptacle with 36 positions arranged in 2 rows on a 0.50mm pitch. It uses center strip contacts with gold plating (8.00µin thickness) and mounts via surface mount. The mated stacking height options are 3.5mm, 4mm, or 5mm, which gives you some flexibility in board spacing for mezzanine designs.
Pitch and footprint — what to check
The 0.50mm pitch is tight — make sure your board layout has the matching footprint and that the solder paste stencil is dialed in for that pitch. The 36 positions in two rows mean the connector is 18 per row, so the overall length is about 9mm plus the end ribs. Confirm the keep-out area on your board clears the connector body.