Extensions 1→N→G→Q→1 with N=C₂²×C₆ and Q=D₇

Direct product G=N×Q with N=C₂²×C₆ and Q=D₇

		d	ρ	Label	ID
D₇×C₂²×C₆		168		D7xC2^2xC6	336,225

Semidirect products G=N:Q with N=C₂²×C₆ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆)⋊₁D₇ = C₆×C₇⋊D₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂²×C₆	168		(C2^2xC6):1D7	336,183
(C₂²×C₆)⋊₂D₇ = C₂×C₂₁⋊₇D₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂²×C₆	168		(C2^2xC6):2D7	336,203
(C₂²×C₆)⋊₃D₇ = C₂³×D₂₁	φ: D₇/C₇ → C₂ ⊆ Aut C₂²×C₆	168		(C2^2xC6):3D7	336,227

Non-split extensions G=N.Q with N=C₂²×C₆ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆).₁D₇ = C₃×C₂³.D₇	φ: D₇/C₇ → C₂ ⊆ Aut C₂²×C₆	168		(C2^2xC6).1D7	336,73
(C₂²×C₆).₂D₇ = C₄₂.₃₈D₄	φ: D₇/C₇ → C₂ ⊆ Aut C₂²×C₆	168		(C2^2xC6).2D7	336,105
(C₂²×C₆).₃D₇ = C₂²×Dic₂₁	φ: D₇/C₇ → C₂ ⊆ Aut C₂²×C₆	336		(C2^2xC6).3D7	336,202
(C₂²×C₆).₄D₇ = C₂×C₆×Dic₇	central extension (φ=1)	336		(C2^2xC6).4D7	336,182

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁