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

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

		d	ρ	Label	ID
C₆×C₁₂		72		C6xC12	72,36

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂⋊₁C₆ = C₃×D₁₂	φ: C₆/C₃ → C₂ ⊆ Aut C₁₂	24	2	C12:1C6	72,28
C₁₂⋊₂C₆ = S₃×C₁₂	φ: C₆/C₃ → C₂ ⊆ Aut C₁₂	24	2	C12:2C6	72,27
C₁₂⋊₃C₆ = D₄×C₃²	φ: C₆/C₃ → C₂ ⊆ Aut C₁₂	36		C12:3C6	72,37

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂.₁C₆ = C₃×Dic₆	φ: C₆/C₃ → C₂ ⊆ Aut C₁₂	24	2	C12.1C6	72,26
C₁₂.₂C₆ = C₃×C₃⋊C₈	φ: C₆/C₃ → C₂ ⊆ Aut C₁₂	24	2	C12.2C6	72,12
C₁₂.₃C₆ = D₄×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₁₂	36	2	C12.3C6	72,10
C₁₂.₄C₆ = Q₈×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₁₂	72	2	C12.4C6	72,11
C₁₂.₅C₆ = Q₈×C₃²	φ: C₆/C₃ → C₂ ⊆ Aut C₁₂	72		C12.5C6	72,38

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁