Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂×C₅₆

Direct product G=N×Q with N=C₄ and Q=C₂×C₅₆

		d	ρ	Label	ID
C₂×C₄×C₅₆		448		C2xC4xC56	448,810

Semidirect products G=N:Q with N=C₄ and Q=C₂×C₅₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₂×C₅₆) = D₄×C₅₆	φ: C₂×C₅₆/C₅₆ → C₂ ⊆ Aut C₄	224		C4:1(C2xC56)	448,842
C₄⋊₂(C₂×C₅₆) = C₁₄×C₄⋊C₈	φ: C₂×C₅₆/C₂×C₂₈ → C₂ ⊆ Aut C₄	448		C4:2(C2xC56)	448,830

Non-split extensions G=N.Q with N=C₄ and Q=C₂×C₅₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂×C₅₆) = C₇×D₄⋊C₈	φ: C₂×C₅₆/C₅₆ → C₂ ⊆ Aut C₄	224		C4.1(C2xC56)	448,129
C₄.₂(C₂×C₅₆) = C₇×Q₈⋊C₈	φ: C₂×C₅₆/C₅₆ → C₂ ⊆ Aut C₄	448		C4.2(C2xC56)	448,130
C₄.₃(C₂×C₅₆) = C₇×D₄.C₈	φ: C₂×C₅₆/C₅₆ → C₂ ⊆ Aut C₄	224	2	C4.3(C2xC56)	448,154
C₄.₄(C₂×C₅₆) = Q₈×C₅₆	φ: C₂×C₅₆/C₅₆ → C₂ ⊆ Aut C₄	448		C4.4(C2xC56)	448,853
C₄.₅(C₂×C₅₆) = C₇×D₄○C₁₆	φ: C₂×C₅₆/C₅₆ → C₂ ⊆ Aut C₄	224	2	C4.5(C2xC56)	448,912
C₄.₆(C₂×C₅₆) = C₇×C₈⋊₂C₈	φ: C₂×C₅₆/C₂×C₂₈ → C₂ ⊆ Aut C₄	448		C4.6(C2xC56)	448,138
C₄.₇(C₂×C₅₆) = C₇×C₈⋊₁C₈	φ: C₂×C₅₆/C₂×C₂₈ → C₂ ⊆ Aut C₄	448		C4.7(C2xC56)	448,139
C₄.₈(C₂×C₅₆) = C₇×C₈.C₈	φ: C₂×C₅₆/C₂×C₂₈ → C₂ ⊆ Aut C₄	112	2	C4.8(C2xC56)	448,168
C₄.₉(C₂×C₅₆) = C₇×C₄².₁₂C₄	φ: C₂×C₅₆/C₂×C₂₈ → C₂ ⊆ Aut C₄	224		C4.9(C2xC56)	448,839
C₄.₁₀(C₂×C₅₆) = C₁₄×M₅(2)	φ: C₂×C₅₆/C₂×C₂₈ → C₂ ⊆ Aut C₄	224		C4.10(C2xC56)	448,911
C₄.₁₁(C₂×C₅₆) = C₇×C₈⋊C₈	central extension (φ=1)	448		C4.11(C2xC56)	448,126
C₄.₁₂(C₂×C₅₆) = C₇×C₁₆⋊₅C₄	central extension (φ=1)	448		C4.12(C2xC56)	448,150
C₄.₁₃(C₂×C₅₆) = C₇×M₆(2)	central extension (φ=1)	224	2	C4.13(C2xC56)	448,174

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