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The Fourth Janko Group$
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Alexander A. Ivanov

Print publication date: 2004

Print ISBN-13: 9780198527596

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198527596.001.0001

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PENTAD GROUP 23+12 · (L 3(2) × Sym5)

PENTAD GROUP 23+12 · (L 3(2) × Sym5)

Chapter:
(p.49) 4 PENTAD GROUP 23+12 · (L 3(2) × Sym5)
Source:
The Fourth Janko Group
Author(s):

A. A. Ivanov

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198527596.003.0004

This chapter discusses the geometric subgroup at level 2 of the modified amalgam G, known as the pentad group, which has a rather complicated structure. The structure can be described in terms of the non-singular 4-dimensional symplectic space over GF(2) and the associated orthogonal spaces. This makes the pentad group an example of a class of so-called tri-extraspecial groups studied by S. V. Shpectorov and the author in another book.

Keywords:   pentad group, geometric subgroups, kernels, cohomology, trident group, automorphism

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