Dixon's character table algorithm revisited
In 1967 the reviewer described an algorithm for computing the ordinary characters of a finite group from the class matrices using finite fields [\textit{J. D. Dixon}, Numer. Math. 10, 446-450 (1967; Zbl 0166.29002)], and an implementation of this algorithm has been available to users of the group theory system CAYLEY. In the present paper the author describes modifications to the algorithm which reduce the number of (expensive) computations of the class matrices. These produce dramatic improvements in the running time. The algorithm is still only useful for groups with relatively small order or with relatively few conjugacy classes. However, examples given show that the 12 characters of the Mathieu group \(M(22)\) could be computed in 563 seconds, and the 88 characters of the Burnside group \(B(2,4)\) of order \(2^{12}\) could be computed in 87 seconds. The modified algorithm is implemented in the current version of CAYLEY.
scientific article; zbMATH DE number 4148390