Extensions 1→N→G→Q→1 with N=D₅₆ and Q=C₂

Direct product G=N×Q with N=D₅₆ and Q=C₂

		d	ρ	Label	ID
C₂×D₅₆		112		C2xD56	224,98

Semidirect products G=N:Q with N=D₅₆ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₅₆⋊₁C₂ = D₁₁₂	φ: C₂/C₁ → C₂ ⊆ Out D₅₆	112	2+	D56:1C2	224,5
D₅₆⋊₂C₂ = C₈⋊D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆	56	4+	D56:2C2	224,103
D₅₆⋊₃C₂ = C₇⋊D₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₅₆	112	4+	D56:3C2	224,32
D₅₆⋊₄C₂ = D₇×D₈	φ: C₂/C₁ → C₂ ⊆ Out D₅₆	56	4+	D56:4C2	224,105
D₅₆⋊₅C₂ = Q₈.D₁₄	φ: C₂/C₁ → C₂ ⊆ Out D₅₆	112	4+	D56:5C2	224,114
D₅₆⋊₆C₂ = D₅₆⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out D₅₆	56	4+	D56:6C2	224,109
D₅₆⋊₇C₂ = D₅₆⋊₇C₂	φ: trivial image	112	2	D56:7C2	224,99

Non-split extensions G=N.Q with N=D₅₆ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₅₆.₁C₂ = C₁₁₂⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out D₅₆	112	2	D56.1C2	224,6
D₅₆.₂C₂ = C₇⋊SD₃₂	φ: C₂/C₁ → C₂ ⊆ Out D₅₆	112	4+	D56.2C2	224,34

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁