Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₁₂

Direct product G=N×Q with N=C₂³ and Q=C₁₂

		d	ρ	Label	ID
C₂³×C₁₂		96		C2^3xC12	96,220

Semidirect products G=N:Q with N=C₂³ and Q=C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊C₁₂ = C₃×C₂³⋊C₄	φ: C₁₂/C₃ → C₄ ⊆ Aut C₂³	24	4	C2^3:C12	96,49
C₂³⋊₂C₁₂ = C₂×C₄×A₄	φ: C₁₂/C₄ → C₃ ⊆ Aut C₂³	24		C2^3:2C12	96,196
C₂³⋊₃C₁₂ = C₆×C₂²⋊C₄	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂³	48		C2^3:3C12	96,162

Non-split extensions G=N.Q with N=C₂³ and Q=C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.C₁₂ = C₃×C₄.D₄	φ: C₁₂/C₃ → C₄ ⊆ Aut C₂³	24	4	C2^3.C12	96,50
C₂³.₂C₁₂ = C₈×A₄	φ: C₁₂/C₄ → C₃ ⊆ Aut C₂³	24	3	C2^3.2C12	96,73
C₂³.₃C₁₂ = C₃×C₂²⋊C₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂³	48		C2^3.3C12	96,48
C₂³.₄C₁₂ = C₆×M₄(2)	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂³	48		C2^3.4C12	96,177

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁