By John Horton Conway
This atlas covers teams from the households of the category of finite easy teams. lately up-to-date incorporating corrections
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Additional resources for Atlas of finite groups: maximal subgroups and ordinary characters for simple groups
1. Format Tables with columns of randomly varying widths have a 'ragged' appearance which is very wearying to the reader. In our tables the only permitted widths are 4, 6, 8, ... spaces. We have taken great pains, particularly with our irrationality conventions, to ensure that most columns will fit into the standard width of 4 spaces, so that large tracts of table have a regular layout. The even-width requirement entails that a wider column is seen to be wider----<:olumns whose widths are nearly but not quite equal producea slightly disorienting effect.
Such a family behaves in many ways like a single N conjugacy class with centralizer order D . The entry in the class name row consists of the order n of the elements concerned, followed by the tag letters of the first and last classes in the family. The remaining entries in the appropriate column refer only to the first class in the family. So in our table for L 3 (8) (page 74), the column beginning @ 3528/6 A A 7AF refers to class 7 A, and tells us that this class is the only printed representative of the 6 classes 7 A, 7 B, 7 C, 7D, 7E, 7F, all having centralizer order 3528.
The merits of such arrangements are usually more evident to the compiler than the user, who is seldom properly informed about the principles (if any) of the arrangement, and so cannot use the implied power map information. It is better to choose a simpler arrangement, and explicitly indicate the power maps. A§, the conjugacy classes within a given coset are arranged firstly, by increasing succession of n, the order of their elements; secondly, for elements with the same n, by decreasing succession of N, their centralizer order; thirdly, for elements with the same nand N, by increasing succession of d, the degree of the algebraic number field generated by their character values (so that rational elements come first); and fourthly, for elements with the same n, N, and d, in a manner which seems best compatible with the p' parts, so that, other things being equal, we prefer to arrange elements of order 10 in the same succession as the elements of order 5 that are their odd parts.