Extensions 1→N→G→Q→1 with N=C₅₆ and Q=C₈

Direct product G=N×Q with N=C₅₆ and Q=C₈

		d	ρ	Label	ID
C₈×C₅₆		448		C8xC56	448,125

Semidirect products G=N:Q with N=C₅₆ and Q=C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆⋊₁C₈ = C₅₆⋊₁C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56:1C8	448,15
C₅₆⋊₂C₈ = C₅₆⋊₂C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56:2C8	448,14
C₅₆⋊₃C₈ = C₈×C₇⋊C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56:3C8	448,10
C₅₆⋊₄C₈ = C₅₆⋊C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56:4C8	448,12
C₅₆⋊₅C₈ = C₇×C₈⋊₁C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56:5C8	448,139
C₅₆⋊₆C₈ = C₇×C₈⋊₂C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56:6C8	448,138
C₅₆⋊₇C₈ = C₇×C₈⋊C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56:7C8	448,126

Non-split extensions G=N.Q with N=C₅₆ and Q=C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆.₁C₈ = C₅₆.₁₆Q₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	112	2	C56.1C8	448,20
C₅₆.₂C₈ = C₇⋊C₆₄	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	448	2	C56.2C8	448,1
C₅₆.₃C₈ = C₄×C₇⋊C₁₆	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56.3C8	448,17
C₅₆.₄C₈ = C₅₆.C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56.4C8	448,18
C₅₆.₅C₈ = C₂×C₇⋊C₃₂	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56.5C8	448,55
C₅₆.₆C₈ = C₇⋊M₆(2)	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	224	2	C56.6C8	448,56
C₅₆.₇C₈ = C₇×C₈.C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	112	2	C56.7C8	448,168
C₅₆.₈C₈ = C₇×C₁₆⋊₅C₄	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56.8C8	448,150
C₅₆.₉C₈ = C₇×M₆(2)	φ: C₈/C₄ → C₂ ⊆ Aut C₅₆	224	2	C56.9C8	448,174

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