By John Horton Conway
This atlas covers teams from the households of the category of finite uncomplicated teams. lately up to date incorporating corrections
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Men who are acquainted with the innumerable difficulties attending the execution of a work of such an extensive nature will make proper allowances. To these we appeal, and shall rest satisfied with the judgement they pronounce. Preface to the first edition of the Encyclopaedia Brittanica, 1771 Our fairly wide experience has taught us that published character tables are as likely as not to contain errors (which are usually minor). A§ appears in print. We first briefly comment on the information not contained in the character tables.
Xxxiii My own function was to initiate and control the entire project, to collaborate with each of the above, and (eventually) to write this Introduction. John Conway November 1984 Department of Pure Mathematics and Mathematical Statistics, University of Cambridge THE GROUPS Alternating group A5 ; Linear group L2 (4) = A1(5) = U2 (5) Linear group L2 (5) Order =A1(4) =U2(4) - S2(5) = 60 = 22. G is the group of those quaternions q for which the coordinates of 2q are (±2,O,O,O)A, (±1,±1,±1,±1), (O,±1,±bS,±bS*)A; these generate the icosian ring G x 2 : symm€tries of the vectors (O,±1,±bS*)C (vertices of icosahedron), or of (±1,±1,±1), Icosahedral (O,±b5*,±bS)C (dodecahedron), or of (±2,O,O)C, (±1,±b5,±bS*)C (icosidodecahedron: the reflections in these generate G x 2).
243-51 is restricted to the 26 sporadic groups, and to a number of books and papers which give information about most or all of the infinite families of simple groups. The works by Gorenstein and Davis in the latter portion are very much more extensive bibliographies. It is a pleasure to record our indebtedness to many colleagues throughout the world who have freely sent us information. We mention particularly our major sources of character tables: M. Hall, Jr Zia-ud-Din A. O. Morris J. A. Todd D.