Extensions 1→N→G→Q→1 with N=C₄ and Q=D₅₄

Direct product G=N×Q with N=C₄ and Q=D₅₄

		d	ρ	Label	ID
C₂×C₄×D₂₇		216		C2xC4xD27	432,44

Semidirect products G=N:Q with N=C₄ and Q=D₅₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁D₅₄ = D₄×D₂₇	φ: D₅₄/D₂₇ → C₂ ⊆ Aut C₄	108	4+	C4:1D54	432,47
C₄⋊₂D₅₄ = C₂×D₁₀₈	φ: D₅₄/C₅₄ → C₂ ⊆ Aut C₄	216		C4:2D54	432,45

Non-split extensions G=N.Q with N=C₄ and Q=D₅₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁D₅₄ = D₄.D₂₇	φ: D₅₄/D₂₇ → C₂ ⊆ Aut C₄	216	4-	C4.1D54	432,15
C₄.₂D₅₄ = D₄⋊D₂₇	φ: D₅₄/D₂₇ → C₂ ⊆ Aut C₄	216	4+	C4.2D54	432,16
C₄.₃D₅₄ = C₂₇⋊Q₁₆	φ: D₅₄/D₂₇ → C₂ ⊆ Aut C₄	432	4-	C4.3D54	432,17
C₄.₄D₅₄ = Q₈⋊₂D₂₇	φ: D₅₄/D₂₇ → C₂ ⊆ Aut C₄	216	4+	C4.4D54	432,18
C₄.₅D₅₄ = D₄⋊₂D₂₇	φ: D₅₄/D₂₇ → C₂ ⊆ Aut C₄	216	4-	C4.5D54	432,48
C₄.₆D₅₄ = Q₈×D₂₇	φ: D₅₄/D₂₇ → C₂ ⊆ Aut C₄	216	4-	C4.6D54	432,49
C₄.₇D₅₄ = Q₈⋊₃D₂₇	φ: D₅₄/D₂₇ → C₂ ⊆ Aut C₄	216	4+	C4.7D54	432,50
C₄.₈D₅₄ = Dic₁₀₈	φ: D₅₄/C₅₄ → C₂ ⊆ Aut C₄	432	2-	C4.8D54	432,4
C₄.₉D₅₄ = C₂₁₆⋊C₂	φ: D₅₄/C₅₄ → C₂ ⊆ Aut C₄	216	2	C4.9D54	432,7
C₄.₁₀D₅₄ = D₂₁₆	φ: D₅₄/C₅₄ → C₂ ⊆ Aut C₄	216	2+	C4.10D54	432,8
C₄.₁₁D₅₄ = C₂×Dic₅₄	φ: D₅₄/C₅₄ → C₂ ⊆ Aut C₄	432		C4.11D54	432,43
C₄.₁₂D₅₄ = D₁₀₈⋊₅C₂	φ: D₅₄/C₅₄ → C₂ ⊆ Aut C₄	216	2	C4.12D54	432,46
C₄.₁₃D₅₄ = C₈×D₂₇	central extension (φ=1)	216	2	C4.13D54	432,5
C₄.₁₄D₅₄ = C₈⋊D₂₇	central extension (φ=1)	216	2	C4.14D54	432,6
C₄.₁₅D₅₄ = C₂×C₂₇⋊C₈	central extension (φ=1)	432		C4.15D54	432,9
C₄.₁₆D₅₄ = C₄.Dic₂₇	central extension (φ=1)	216	2	C4.16D54	432,10

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