Extensions 1→N→G→Q→1 with N=C₂⁴ and Q=C₄

Direct product G=N×Q with N=C₂⁴ and Q=C₄

		d	ρ	Label	ID
C₂⁴×C₄		64		C2^4xC4	64,260

Semidirect products G=N:Q with N=C₂⁴ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴⋊₁C₄ = C₂≀C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂⁴	8	4+	C2^4:1C4	64,32
C₂⁴⋊₂C₄ = C₂×C₂³⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂⁴	16		C2^4:2C4	64,90
C₂⁴⋊₃C₄ = C₂⁴⋊₃C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂⁴	16		C2^4:3C4	64,60
C₂⁴⋊₄C₄ = C₂²×C₂²⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂⁴	32		C2^4:4C4	64,193

Non-split extensions G=N.Q with N=C₂⁴ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴.₁C₄ = C₂³⋊C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₂⁴	16		C2^4.1C4	64,4
C₂⁴.₂C₄ = C₂×C₄.D₄	φ: C₄/C₁ → C₄ ⊆ Aut C₂⁴	16		C2^4.2C4	64,92
C₂⁴.₃C₄ = C₂×C₂²⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₂⁴	32		C2^4.3C4	64,87
C₂⁴.₄C₄ = C₂⁴.₄C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₂⁴	16		C2^4.4C4	64,88
C₂⁴.₅C₄ = C₂²×M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₂⁴	32		C2^4.5C4	64,247

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁