1. A computer system, comprising: a configuration comprising one or more cores configurable between a single thread (ST) mode and a multithreading (MT) mode, the ST mode addressing a primary thread and the MT mode addressing the primary thread and one or more secondary threads on shared resources of each core; and a multithreading facility configured to control utilization of the configuration to perform a method comprising: executing, by a core, a retrieve multithreading capability information (RMTCI) instruction, the execution comprising: obtaining thread identification information that identifies multithreading capability of the configuration; and storing the obtained thread identification information.