Endomorphism structure of groups of order 8

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This article gives specific information, namely, element structure, about a family of groups, namely: groups of order 8.
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Automorphism groups

Group GAP ID (second part) Order of automorphism group Iso. class of automorphism group Log_2 of largest power of 2 dividing automorphism group order Iso. class of 2-Sylow subgroup of automorphism group Log_2 of order of 2-core Iso. class of 2-core Log_2 of order of inner automorphism group Iso. class of inner automorphism group
cyclic group:Z8 1 4 Klein four-group 2 Klein four-group 2 Klein four-group 0 trivial group
direct product of Z4 and Z2 2 8 dihedral group:D8 3 dihedral group:D8 3 dihedral group:D8 0 trivial group
dihedral group:D8 3 8 dihedral group:D8 3 dihedral group:D8 3 dihedral group:D8 2 Klein four-group
quaternion group 4 24 symmetric group:S4 3 dihedral group:D8 2 Klein four-group 2 Klein four-group
elementary abelian group:E8 5 168 general linear group:GL(3,2) 3 dihedral group:D8 0 trivial group 0 trivial group