Extensions 1→N→G→Q→1 with N=C₃² and Q=F₇

Direct product G=N×Q with N=C₃² and Q=F₇

		d	ρ	Label	ID
C₃²×F₇		63		C3^2xF7	378,47

Semidirect products G=N:Q with N=C₃² and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊F₇ = C₃²⋊F₇	φ: F₇/C₇ → C₆ ⊆ Aut C₃²	63	6+	C3^2:F7	378,22
C₃²⋊₂F₇ = D₇⋊He₃	φ: F₇/D₇ → C₃ ⊆ Aut C₃²	63	6	C3^2:2F7	378,12
C₃²⋊₃F₇ = C₃×C₃⋊F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₃²	42	6	C3^2:3F7	378,49
C₃²⋊₄F₇ = C₃²⋊₄F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₃²	63		C3^2:4F7	378,51

Non-split extensions G=N.Q with N=C₃² and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².F₇ = C₃².F₇	φ: F₇/D₇ → C₃ ⊆ Aut C₃²	63	6	C3^2.F7	378,11
C₃².₂F₇ = D₂₁⋊C₉	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₃²	126	6	C3^2.2F7	378,21
C₃².₃F₇ = C₃×C₇⋊C₁₈	central extension (φ=1)	189		C3^2.3F7	378,10

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁