Extensions 1→N→G→Q→1 with N=C₂² and Q=F₇

Direct product G=N×Q with N=C₂² and Q=F₇

		d	ρ	Label	ID
C₂²×F₇		28		C2^2xF7	168,47

Semidirect products G=N:Q with N=C₂² and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊F₇ = D₇⋊A₄	φ: F₇/D₇ → C₃ ⊆ Aut C₂²	28	6+	C2^2:F7	168,49
C₂²⋊₂F₇ = Dic₇⋊C₆	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₂²	28	6	C2^2:2F7	168,11

Non-split extensions G=N.Q with N=C₂² and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².F₇ = C₂×C₇⋊C₁₂	central extension (φ=1)	56		C2^2.F7	168,10

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C22 and Q=F7