Extensions 1→N→G→Q→1 with N=C₅₆ and Q=C₂

Direct product G=N×Q with N=C₅₆ and Q=C₂

		d	ρ	Label	ID
C₂×C₅₆		112		C2xC56	112,22

Semidirect products G=N:Q with N=C₅₆ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆⋊₁C₂ = D₅₆	φ: C₂/C₁ → C₂ ⊆ Aut C₅₆	56	2+	C56:1C2	112,6
C₅₆⋊₂C₂ = C₅₆⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₅₆	56	2	C56:2C2	112,5
C₅₆⋊₃C₂ = C₈×D₇	φ: C₂/C₁ → C₂ ⊆ Aut C₅₆	56	2	C56:3C2	112,3
C₅₆⋊₄C₂ = C₈⋊D₇	φ: C₂/C₁ → C₂ ⊆ Aut C₅₆	56	2	C56:4C2	112,4
C₅₆⋊₅C₂ = C₇×D₈	φ: C₂/C₁ → C₂ ⊆ Aut C₅₆	56	2	C56:5C2	112,24
C₅₆⋊₆C₂ = C₇×SD₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₅₆	56	2	C56:6C2	112,25
C₅₆⋊₇C₂ = C₇×M₄(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₅₆	56	2	C56:7C2	112,23

Non-split extensions G=N.Q with N=C₅₆ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆.₁C₂ = Dic₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₅₆	112	2-	C56.1C2	112,7
C₅₆.₂C₂ = C₇⋊C₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₅₆	112	2	C56.2C2	112,1
C₅₆.₃C₂ = C₇×Q₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₅₆	112	2	C56.3C2	112,26

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