Extensions 1→N→G→Q→1 with N=C₁₀ and Q=F₇

Direct product G=N×Q with N=C₁₀ and Q=F₇

		d	ρ	Label	ID
C₁₀×F₇		70	6	C10xF7	420,17

Semidirect products G=N:Q with N=C₁₀ and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊F₇ = C₂×C₅⋊F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₁₀	70	6+	C10:F7	420,19

Non-split extensions G=N.Q with N=C₁₀ and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.F₇ = C₃₅⋊₃C₁₂	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₁₀	140	6-	C10.F7	420,3
C₁₀.₂F₇ = C₅×C₇⋊C₁₂	central extension (φ=1)	140	6	C10.2F7	420,1

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C10 and Q=F7