Extensions 1→N→G→Q→1 with N=C₅₄ and Q=D₄

Direct product G=N×Q with N=C₅₄ and Q=D₄

		d	ρ	Label	ID
D₄×C₅₄		216		D4xC54	432,54

Semidirect products G=N:Q with N=C₅₄ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₄⋊₁D₄ = C₂×D₁₀₈	φ: D₄/C₄ → C₂ ⊆ Aut C₅₄	216		C54:1D4	432,45
C₅₄⋊₂D₄ = C₂×C₂₇⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₄	216		C54:2D4	432,52

Non-split extensions G=N.Q with N=C₅₄ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₄.₁D₄ = Dic₁₀₈	φ: D₄/C₄ → C₂ ⊆ Aut C₅₄	432	2-	C54.1D4	432,4
C₅₄.₂D₄ = C₂₁₆⋊C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₅₄	216	2	C54.2D4	432,7
C₅₄.₃D₄ = D₂₁₆	φ: D₄/C₄ → C₂ ⊆ Aut C₅₄	216	2+	C54.3D4	432,8
C₅₄.₄D₄ = C₄⋊Dic₂₇	φ: D₄/C₄ → C₂ ⊆ Aut C₅₄	432		C54.4D4	432,13
C₅₄.₅D₄ = Dic₂₇⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₄	432		C54.5D4	432,12
C₅₄.₆D₄ = D₅₄⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₄	216		C54.6D4	432,14
C₅₄.₇D₄ = D₄.D₂₇	φ: D₄/C₂² → C₂ ⊆ Aut C₅₄	216	4-	C54.7D4	432,15
C₅₄.₈D₄ = D₄⋊D₂₇	φ: D₄/C₂² → C₂ ⊆ Aut C₅₄	216	4+	C54.8D4	432,16
C₅₄.₉D₄ = C₂₇⋊Q₁₆	φ: D₄/C₂² → C₂ ⊆ Aut C₅₄	432	4-	C54.9D4	432,17
C₅₄.₁₀D₄ = Q₈⋊₂D₂₇	φ: D₄/C₂² → C₂ ⊆ Aut C₅₄	216	4+	C54.10D4	432,18
C₅₄.₁₁D₄ = C₅₄.D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₄	216		C54.11D4	432,19
C₅₄.₁₂D₄ = C₂²⋊C₄×C₂₇	central extension (φ=1)	216		C54.12D4	432,21
C₅₄.₁₃D₄ = C₄⋊C₄×C₂₇	central extension (φ=1)	432		C54.13D4	432,22
C₅₄.₁₄D₄ = D₈×C₂₇	central extension (φ=1)	216	2	C54.14D4	432,25
C₅₄.₁₅D₄ = SD₁₆×C₂₇	central extension (φ=1)	216	2	C54.15D4	432,26
C₅₄.₁₆D₄ = Q₁₆×C₂₇	central extension (φ=1)	432	2	C54.16D4	432,27

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