Extensions 1→N→G→Q→1 with N=C₆ and Q=C₃×C₁₂

Direct product G=N×Q with N=C₆ and Q=C₃×C₁₂

		d	ρ	Label	ID
C₃×C₆×C₁₂		216		C3xC6xC12	216,150

Semidirect products G=N:Q with N=C₆ and Q=C₃×C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊(C₃×C₁₂) = Dic₃×C₃×C₆	φ: C₃×C₁₂/C₃×C₆ → C₂ ⊆ Aut C₆	72		C6:(C3xC12)	216,138

Non-split extensions G=N.Q with N=C₆ and Q=C₃×C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.(C₃×C₁₂) = C₃²×C₃⋊C₈	φ: C₃×C₁₂/C₃×C₆ → C₂ ⊆ Aut C₆	72		C6.(C3xC12)	216,82
C₆.₂(C₃×C₁₂) = C₈×He₃	central extension (φ=1)	72	3	C6.2(C3xC12)	216,19
C₆.₃(C₃×C₁₂) = C₈×3_-¹⁺²	central extension (φ=1)	72	3	C6.3(C3xC12)	216,20
C₆.₄(C₃×C₁₂) = C₂×C₄×He₃	central extension (φ=1)	72		C6.4(C3xC12)	216,74
C₆.₅(C₃×C₁₂) = C₂×C₄×3_-¹⁺²	central extension (φ=1)	72		C6.5(C3xC12)	216,75

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁