The TSS GROUP is different than the RACF GROUP.
The RACF GROUP is like a TSS PROFILE but is also used to assign a GID.
In TSS, you assign a GID, by adding the GID to GROUP, then attaching that GROUP to an acid. The TSS GROUP is not used to group entitlement.
PROFILEs are used to group entitlements.
The RACF equivalent in TSS would be to add the GROUP ***AND*** PROFILE to the acid. Example:
TSS ADD(JOE) GROUP(OMVSGRP)
TSS ADD(JOE) PROFILE(TRANPROF)