Wet-Running Multi-Disk Clutch and Motor Vehicle Transmission

A wet-running multi-disk clutch (B) for a motor vehicle transmission (G), comprising:

• an inner disk carrier (ILT, HO);
• a plurality of inner clutch disks (IL) connected to the inner disk carrier (ILT, HO) via an inner tooth system (ILZ);
• an outer disk carrier (ALT, GG);
• a plurality of outer clutch disks (AL, ALE) connected to the outer disk carrier (ALT, GG) via an outer tooth system (ALZ), the outer clutch disks (AL) arranged in alternation with the inner clutch disks (IL);
• and
• a piston (K) provided at a first side of the multi-disk clutch (B), the piston configured to apply a force acting an axial direction onto the inner and outer clutch disks (IL, AL) in order to engage the multi-disk clutch (B),
• wherein the multi-disk clutch (B) is supportable against an abutting surface (AF) via an end disk (ALE) of the outer clutch disks (AL) at a second side of the multi-disk clutch (B) that is opposite the first side of the multi-disk clutch (B), and
• wherein a plurality of grooves (N) are provided at one or both of the abutting surface (AF) and the end disk (ALE), the grooves (N) configured and arranged such that cooling fluid (O) routed to the multi-disk clutch (B) is flowable out of the multi-disk clutch (B) through the grooves (N).