Extensions 1→N→G→Q→1 with N=C₅₀ and Q=C₂³

Direct product G=N×Q with N=C₅₀ and Q=C₂³

		d	ρ	Label	ID
C₂³×C₅₀		400		C2^3xC50	400,55

Semidirect products G=N:Q with N=C₅₀ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₀⋊C₂³ = C₂³×D₂₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₀	200		C50:C2^3	400,54

Non-split extensions G=N.Q with N=C₅₀ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₀.₁C₂³ = C₂×Dic₅₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₀	400		C50.1C2^3	400,35
C₅₀.₂C₂³ = C₂×C₄×D₂₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₀	200		C50.2C2^3	400,36
C₅₀.₃C₂³ = C₂×D₁₀₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₀	200		C50.3C2^3	400,37
C₅₀.₄C₂³ = D₁₀₀⋊₅C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₀	200	2	C50.4C2^3	400,38
C₅₀.₅C₂³ = D₄×D₂₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₀	100	4+	C50.5C2^3	400,39
C₅₀.₆C₂³ = D₄⋊₂D₂₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₀	200	4-	C50.6C2^3	400,40
C₅₀.₇C₂³ = Q₈×D₂₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₀	200	4-	C50.7C2^3	400,41
C₅₀.₈C₂³ = Q₈⋊₂D₂₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₀	200	4+	C50.8C2^3	400,42
C₅₀.₉C₂³ = C₂²×Dic₂₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₀	400		C50.9C2^3	400,43
C₅₀.₁₀C₂³ = C₂×C₂₅⋊D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₀	200		C50.10C2^3	400,44
C₅₀.₁₁C₂³ = D₄×C₅₀	central extension (φ=1)	200		C50.11C2^3	400,46
C₅₀.₁₂C₂³ = Q₈×C₅₀	central extension (φ=1)	400		C50.12C2^3	400,47
C₅₀.₁₃C₂³ = C₄○D₄×C₂₅	central extension (φ=1)	200	2	C50.13C2^3	400,48

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