This book classifies the maximal subgroups of the almost simple
finite classical groups in dimension up to 12; it also describes
the maximal subgroups of the almost simple finite exceptional
groups with socle one of Sz(q), G2(q), 2G2(q) or 3D4(q).
Theoretical and computational tools are used throughout, with
downloadable Magma code provided. The exposition contains a wealth
of information on the structure and action of the geometric
subgroups of classical groups, but the reader will also encounter
methods for analysing the structure and maximality of almost simple
subgroups of almost simple groups. Additionally, this book contains
detailed information on using Magma to calculate with
representations over number fields and finite fields. Featured
within are previously unseen results and over 80 tables describing
the maximal subgroups, making this volume an essential reference
for researchers. It also functions as a graduate-level textbook on
finite simple groups, computational group theory and representation
theory.
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