Extensions 1→N→G→Q→1 with N=C₂⁴ and Q=C₁₂

Direct product G=N×Q with N=C₂⁴ and Q=C₁₂

		d	ρ	Label	ID
C₂⁴×C₁₂		192		C2^4xC12	192,1530

Semidirect products G=N:Q with N=C₂⁴ and Q=C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴⋊₁C₁₂ = C₂⁴⋊C₁₂	φ: C₁₂/C₂ → C₆ ⊆ Aut C₂⁴	12	6+	C2^4:1C12	192,191
C₂⁴⋊₂C₁₂ = A₄×C₂²⋊C₄	φ: C₁₂/C₂ → C₆ ⊆ Aut C₂⁴	24		C2^4:2C12	192,994
C₂⁴⋊₃C₁₂ = C₃×C₂≀C₄	φ: C₁₂/C₃ → C₄ ⊆ Aut C₂⁴	24	4	C2^4:3C12	192,157
C₂⁴⋊₄C₁₂ = C₆×C₂³⋊C₄	φ: C₁₂/C₃ → C₄ ⊆ Aut C₂⁴	48		C2^4:4C12	192,842
C₂⁴⋊₅C₁₂ = A₄×C₂²×C₄	φ: C₁₂/C₄ → C₃ ⊆ Aut C₂⁴	48		C2^4:5C12	192,1496
C₂⁴⋊₆C₁₂ = C₄×C₂²⋊A₄	φ: C₁₂/C₄ → C₃ ⊆ Aut C₂⁴	24		C2^4:6C12	192,1505
C₂⁴⋊₇C₁₂ = C₃×C₂⁴⋊₃C₄	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂⁴	48		C2^4:7C12	192,812
C₂⁴⋊₈C₁₂ = C₂×C₆×C₂²⋊C₄	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂⁴	96		C2^4:8C12	192,1401

Non-split extensions G=N.Q with N=C₂⁴ and Q=C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴.C₁₂ = A₄×M₄(2)	φ: C₁₂/C₂ → C₆ ⊆ Aut C₂⁴	24	6	C2^4.C12	192,1011
C₂⁴.₂C₁₂ = C₃×C₂³⋊C₈	φ: C₁₂/C₃ → C₄ ⊆ Aut C₂⁴	48		C2^4.2C12	192,129
C₂⁴.₃C₁₂ = C₆×C₄.D₄	φ: C₁₂/C₃ → C₄ ⊆ Aut C₂⁴	48		C2^4.3C12	192,844
C₂⁴.₄C₁₂ = A₄×C₂×C₈	φ: C₁₂/C₄ → C₃ ⊆ Aut C₂⁴	48		C2^4.4C12	192,1010
C₂⁴.₅C₁₂ = C₆×C₂²⋊C₈	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂⁴	96		C2^4.5C12	192,839
C₂⁴.₆C₁₂ = C₃×C₂⁴.₄C₄	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂⁴	48		C2^4.6C12	192,840
C₂⁴.₇C₁₂ = C₂×C₆×M₄(2)	φ: C₁₂/C₆ → C₂ ⊆ Aut C₂⁴	96		C2^4.7C12	192,1455

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁