Extensions 1→N→G→Q→1 with N=C₄ and Q=D₅₀

Direct product G=N×Q with N=C₄ and Q=D₅₀

		d	ρ	Label	ID
C₂×C₄×D₂₅		200		C2xC4xD25	400,36

Semidirect products G=N:Q with N=C₄ and Q=D₅₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁D₅₀ = D₄×D₂₅	φ: D₅₀/D₂₅ → C₂ ⊆ Aut C₄	100	4+	C4:1D50	400,39
C₄⋊₂D₅₀ = C₂×D₁₀₀	φ: D₅₀/C₅₀ → C₂ ⊆ Aut C₄	200		C4:2D50	400,37

Non-split extensions G=N.Q with N=C₄ and Q=D₅₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁D₅₀ = D₄.D₂₅	φ: D₅₀/D₂₅ → C₂ ⊆ Aut C₄	200	4-	C4.1D50	400,15
C₄.₂D₅₀ = D₄⋊D₂₅	φ: D₅₀/D₂₅ → C₂ ⊆ Aut C₄	200	4+	C4.2D50	400,16
C₄.₃D₅₀ = C₂₅⋊Q₁₆	φ: D₅₀/D₂₅ → C₂ ⊆ Aut C₄	400	4-	C4.3D50	400,17
C₄.₄D₅₀ = Q₈⋊D₂₅	φ: D₅₀/D₂₅ → C₂ ⊆ Aut C₄	200	4+	C4.4D50	400,18
C₄.₅D₅₀ = D₄⋊₂D₂₅	φ: D₅₀/D₂₅ → C₂ ⊆ Aut C₄	200	4-	C4.5D50	400,40
C₄.₆D₅₀ = Q₈×D₂₅	φ: D₅₀/D₂₅ → C₂ ⊆ Aut C₄	200	4-	C4.6D50	400,41
C₄.₇D₅₀ = Q₈⋊₂D₂₅	φ: D₅₀/D₂₅ → C₂ ⊆ Aut C₄	200	4+	C4.7D50	400,42
C₄.₈D₅₀ = Dic₁₀₀	φ: D₅₀/C₅₀ → C₂ ⊆ Aut C₄	400	2-	C4.8D50	400,4
C₄.₉D₅₀ = C₂₀₀⋊C₂	φ: D₅₀/C₅₀ → C₂ ⊆ Aut C₄	200	2	C4.9D50	400,7
C₄.₁₀D₅₀ = D₂₀₀	φ: D₅₀/C₅₀ → C₂ ⊆ Aut C₄	200	2+	C4.10D50	400,8
C₄.₁₁D₅₀ = C₂×Dic₅₀	φ: D₅₀/C₅₀ → C₂ ⊆ Aut C₄	400		C4.11D50	400,35
C₄.₁₂D₅₀ = C₈×D₂₅	central extension (φ=1)	200	2	C4.12D50	400,5
C₄.₁₃D₅₀ = C₈⋊D₂₅	central extension (φ=1)	200	2	C4.13D50	400,6
C₄.₁₄D₅₀ = C₂×C₂₅⋊₂C₈	central extension (φ=1)	400		C4.14D50	400,9
C₄.₁₅D₅₀ = C₄.Dic₂₅	central extension (φ=1)	200	2	C4.15D50	400,10
C₄.₁₆D₅₀ = D₁₀₀⋊₅C₂	central extension (φ=1)	200	2	C4.16D50	400,38

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