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Comparison with the ATLAS table The ATLAS of finite groups (Conway, et. al, 1985) is a reference work that contains information about many simple groups and their close relatives. Amongst other information, it gives the character table of the group. The page for the same group M11 is reproduced here. The letter notation for cyclotomic irrationalities origins in this book and is explained in the preface. The “Construction” section describes some ways how to obtain the group, from scratch or within other groups. A presentation is a set of defining rules for the group, i.e. any relation among elements (as products in generators) is a consequence. For each (class of ) maximal subgroups a representative is listed, together with some structure information, the decomposition of the permutation character on the cosets, and ways to construct such subgroups in the full group. The indicator column gives the FrobeniusSchurIndicator (see future homework) that describes whether the corresponding representation is real. The layout of the table (10 classes here). This is mainly relevant if the table for the group and some extensions are given together. There is no general way to assign names to groups that determine isomorphism type. However sometimes there are just few (or even only one) group with a given composition structure, this happens to hold for many of the more interesting groups. The ATLAS notation uses the form A.B to denote an extension of a normal subgroup A by a factor group B. If the extension is known to be split (semidirect product) a colon : is used. If the extension is known to be not split a high dot ˙is used. Classes are labeled by element order and letters. A name B** indicates that this is a class of suitable powers of the corresponding Aclass. The p-power maps give the classes of powers for the primes dividing the order, i.e. AB for a class of order 6 means that g2 is in class 3A and g3 in class 3B.