A Search for Simple Groups of Orders Less Than One Million

摘要

In 1900 L. E. Dickson listed 53 known simple groups of composite order less than one million. Three more groups have been added to this list since that time. A group of order 29120 was discovered by M. Suzuki in 1960, the first of an infinite class, and one of order 175,560 was discovered by Z. Janko in 1965 which appears to be isolated. Very recently Z. Janko announced that a simple group with certain properties would have order 604,800 and have a specific character table. The construction of a simple group of order 604,800 is given for the first time in this paper.