Experimental Mathematics

Finite subgroups of {${\rm GL}\sb {24}({\bf Q})$}

Gabriele Nebe

Abstract

We classify maximal finite irreducible subgroups of GL$_{\sans{24}} (\Q)$, together with their natural lattices. There are 65 conjugacy classes of such groups, 41 of which consist of primitive groups. New methods for finding the maximal finite supergroups of irreducible cyclic groups are developed and applied.

Article information

Source
Experiment. Math., Volume 5, Issue 3 (1996), 163-195.

Dates
First available in Project Euclid: 17 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1047915100

Mathematical Reviews number (MathSciNet)
MR1426447

Zentralblatt MATH identifier
0870.20029

Subjects
Primary: 20H20: Other matrix groups over fields
Secondary: 20C15: Ordinary representations and characters

Keywords
finite rational matrix groups finite integral matrix groups integral lattices in Euclidean space positive definite integral quadratic forms

Citation

Nebe, Gabriele. Finite subgroups of {${\rm GL}\sb {24}({\bf Q})$}. Experiment. Math. 5 (1996), no. 3, 163--195. https://projecteuclid.org/euclid.em/1047915100


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