Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₅₄

Direct product G=N×Q with N=Q₈ and Q=C₅₄

		d	ρ	Label	ID
Q₈×C₅₄		432		Q8xC54	432,55

Semidirect products G=N:Q with N=Q₈ and Q=C₅₄

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊C₅₄ = C₂×Q₈⋊C₂₇	φ: C₅₄/C₁₈ → C₃ ⊆ Out Q₈	432		Q8:C54	432,41
Q₈⋊₂C₅₄ = SD₁₆×C₂₇	φ: C₅₄/C₂₇ → C₂ ⊆ Out Q₈	216	2	Q8:2C54	432,26
Q₈⋊₃C₅₄ = C₄○D₄×C₂₇	φ: trivial image	216	2	Q8:3C54	432,56

Non-split extensions G=N.Q with N=Q₈ and Q=C₅₄

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.C₅₄ = Q₈.C₅₄	φ: C₅₄/C₁₈ → C₃ ⊆ Out Q₈	216	2	Q8.C54	432,42
Q₈.₂C₅₄ = Q₁₆×C₂₇	φ: C₅₄/C₂₇ → C₂ ⊆ Out Q₈	432	2	Q8.2C54	432,27

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Extensions 1→N→G→Q→1 with N=Q8 and Q=C54