Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₅₆

Direct product G=N×Q with N=C₂³ and Q=C₅₆

		d	ρ	Label	ID
C₂³×C₅₆		448		C2^3xC56	448,1348

Semidirect products G=N:Q with N=C₂³ and Q=C₅₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊C₅₆ = C₈×F₈	φ: C₅₆/C₈ → C₇ ⊆ Aut C₂³	56	7	C2^3:C56	448,919
C₂³⋊₂C₅₆ = C₇×C₂³⋊C₈	φ: C₅₆/C₁₄ → C₄ ⊆ Aut C₂³	112		C2^3:2C56	448,127
C₂³⋊₃C₅₆ = C₁₄×C₂²⋊C₈	φ: C₅₆/C₂₈ → C₂ ⊆ Aut C₂³	224		C2^3:3C56	448,814

Non-split extensions G=N.Q with N=C₂³ and Q=C₅₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.C₅₆ = C₇×C₂³.C₈	φ: C₅₆/C₁₄ → C₄ ⊆ Aut C₂³	112	4	C2^3.C56	448,153
C₂³.₂C₅₆ = C₇×C₂²⋊C₁₆	φ: C₅₆/C₂₈ → C₂ ⊆ Aut C₂³	224		C2^3.2C56	448,152
C₂³.₃C₅₆ = C₁₄×M₅(2)	φ: C₅₆/C₂₈ → C₂ ⊆ Aut C₂³	224		C2^3.3C56	448,911

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Extensions 1→N→G→Q→1 with N=C23 and Q=C56