# Endomorphism structure of elementary abelian group:E8

## Contents

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This article describes the structure of endomorphisms (and in particular automorphisms) of elementary abelian group:E8, which is the elementary abelian group of order 8, or equivalently, the direct product of three copies of cyclic group:Z2.

## Summary of information

Construct Value Order Second part of GAP ID (if applicable)
endomorphism ring matrix ring $M(3,2)$: $3 \times 3$ matrices over field:F2 512 --
automorphism group projective special linear group:PSL(3,2) (which is the same as $GL(3,2)$) 168 42
inner automorphism group trivial group 1 1
outer automorphism group projective special linear group:PSL(3,2) 168 42
extended automorphism group projective special linear group:PSL(3,2) 168 42
quasiautomorphism group projective special linear group:PSL(3,2) 168 42
1-automorphism group symmetric group:S7 5040 -- (order too large)