Extensions 1→N→G→Q→1 with N=C₅₀ and Q=D₄

Direct product G=N×Q with N=C₅₀ and Q=D₄

		d	ρ	Label	ID
D₄×C₅₀		200		D4xC50	400,46

Semidirect products G=N:Q with N=C₅₀ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₀⋊₁D₄ = C₂×D₁₀₀	φ: D₄/C₄ → C₂ ⊆ Aut C₅₀	200		C50:1D4	400,37
C₅₀⋊₂D₄ = C₂×C₂₅⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₀	200		C50:2D4	400,44

Non-split extensions G=N.Q with N=C₅₀ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₀.₁D₄ = Dic₁₀₀	φ: D₄/C₄ → C₂ ⊆ Aut C₅₀	400	2-	C50.1D4	400,4
C₅₀.₂D₄ = C₂₀₀⋊C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₅₀	200	2	C50.2D4	400,7
C₅₀.₃D₄ = D₂₀₀	φ: D₄/C₄ → C₂ ⊆ Aut C₅₀	200	2+	C50.3D4	400,8
C₅₀.₄D₄ = C₄⋊Dic₂₅	φ: D₄/C₄ → C₂ ⊆ Aut C₅₀	400		C50.4D4	400,13
C₅₀.₅D₄ = C₅₀.D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₀	400		C50.5D4	400,12
C₅₀.₆D₄ = D₅₀⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₀	200		C50.6D4	400,14
C₅₀.₇D₄ = D₄.D₂₅	φ: D₄/C₂² → C₂ ⊆ Aut C₅₀	200	4-	C50.7D4	400,15
C₅₀.₈D₄ = D₄⋊D₂₅	φ: D₄/C₂² → C₂ ⊆ Aut C₅₀	200	4+	C50.8D4	400,16
C₅₀.₉D₄ = C₂₅⋊Q₁₆	φ: D₄/C₂² → C₂ ⊆ Aut C₅₀	400	4-	C50.9D4	400,17
C₅₀.₁₀D₄ = Q₈⋊D₂₅	φ: D₄/C₂² → C₂ ⊆ Aut C₅₀	200	4+	C50.10D4	400,18
C₅₀.₁₁D₄ = C₂³.D₂₅	φ: D₄/C₂² → C₂ ⊆ Aut C₅₀	200		C50.11D4	400,19
C₅₀.₁₂D₄ = C₂²⋊C₄×C₂₅	central extension (φ=1)	200		C50.12D4	400,21
C₅₀.₁₃D₄ = C₄⋊C₄×C₂₅	central extension (φ=1)	400		C50.13D4	400,22
C₅₀.₁₄D₄ = D₈×C₂₅	central extension (φ=1)	200	2	C50.14D4	400,25
C₅₀.₁₅D₄ = SD₁₆×C₂₅	central extension (φ=1)	200	2	C50.15D4	400,26
C₅₀.₁₆D₄ = Q₁₆×C₂₅	central extension (φ=1)	400	2	C50.16D4	400,27

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