The Primitive Permutation Groups of Degree Less Than 4096

Abstract

In this article we use the Classification of the Finite Simple Groups, the O'Nan–Scott Theorem, and Aschbacher's theorem to classify the primitive permutation groups of degree less than 4096. The results will be added to the primitive groups databases of GAP and MAGMA.

Key Words:

• Group
• Permutation
• Primitive

2000 Mathematics Subject Classification:

• 20B15

ACKNOWLEDGMENT

The first Author is supported by an EPSRC doctoral training grant. The second and third authors acknowledge the support of EPSRC grant number EP/C523229/1.

Notes

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Communicated by D. Macpherson.