The Nonabelian Simple Groups G, | G | < 10 6 -Maximal Subgroups

J. Fischer, J. McKay
1978 Mathematics of Computation  
The maximal subgroups of all the simple groups (except L(2, q)) of order up to one million are given to within conjugacy. Permutation characters on the cosets of the maximal subgroups are given, as are orbit lengths (whenever practical). Introduction. We present a complete list, to within conjugacy, of the maximal subgroups of each nonabelian simple group G, \G\ > 106, excepting the family L(2, q) for which the subgroups are described in the literature [10] . For each G we calculate its
more » ... ion character on the cosets of each maximal subgroup and the corresponding orbits of the representation restricted to that subgroup. Use was made of the GROUP program [2] on a CDC 6400 computer. Notation. Repeated use is made of the character tables for the simple groups G, \G\ < 106, found in [13] . We refer to the irreducible characters of a group by their degrees and, if necessary, a subscript determined by their order of appearance in these character tables; for example, the irreducible characters of M22 are denoted by 1, 21, 45j, 452, 55, 99, 154, 210, 231, 280j, 2802, 385. We use the following notation:
doi:10.2307/2006354 fatcat:ml3ardurabfzjobmjxj3hgf5ku