Extensions 1→N→G→Q→1 with N=C₃×C₆ and Q=D₇

Direct product G=N×Q with N=C₃×C₆ and Q=D₇

		d	ρ	Label	ID
D₇×C₃×C₆		126		D7xC3xC6	252,41

Semidirect products G=N:Q with N=C₃×C₆ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆)⋊₁D₇ = C₆×D₂₁	φ: D₇/C₇ → C₂ ⊆ Aut C₃×C₆	84	2	(C3xC6):1D7	252,43
(C₃×C₆)⋊₂D₇ = C₂×C₃⋊D₂₁	φ: D₇/C₇ → C₂ ⊆ Aut C₃×C₆	126		(C3xC6):2D7	252,45

Non-split extensions G=N.Q with N=C₃×C₆ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆).₁D₇ = C₃×Dic₂₁	φ: D₇/C₇ → C₂ ⊆ Aut C₃×C₆	84	2	(C3xC6).1D7	252,22
(C₃×C₆).₂D₇ = C₃⋊Dic₂₁	φ: D₇/C₇ → C₂ ⊆ Aut C₃×C₆	252		(C3xC6).2D7	252,24
(C₃×C₆).₃D₇ = C₃²×Dic₇	central extension (φ=1)	252		(C3xC6).3D7	252,20

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3×C6 and Q=D7