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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₄⋊Q₈ = C₂×Dic₅₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₄	432		C54:Q8	432,43

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

extension	φ:Q→Aut N	d	Label	ID
C₅₄.₁Q₈ = Dic₂₇⋊C₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₄	432	C54.1Q8	432,12
C₅₄.₂Q₈ = C₄⋊Dic₂₇	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₄	432	C54.2Q8	432,13
C₅₄.₃Q₈ = C₄⋊C₄×C₂₇	central extension (φ=1)	432	C54.3Q8	432,22

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