Extensions 1→N→G→Q→1 with N=C₅ and Q=C₁₂⋊₃D₄

Direct product G=N×Q with N=C₅ and Q=C₁₂⋊₃D₄

		d	ρ	Label	ID
C₅×C₁₂⋊₃D₄		240		C5xC12:3D4	480,819

Semidirect products G=N:Q with N=C₅ and Q=C₁₂⋊₃D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₁₂⋊₃D₄) = C₁₂⋊D₂₀	φ: C₁₂⋊₃D₄/C₄×Dic₃ → C₂ ⊆ Aut C₅	240		C5:1(C12:3D4)	480,534
C₅⋊₂(C₁₂⋊₃D₄) = C₆₀⋊₁₀D₄	φ: C₁₂⋊₃D₄/C₂×D₁₂ → C₂ ⊆ Aut C₅	240		C5:2(C12:3D4)	480,539
C₅⋊₃(C₁₂⋊₃D₄) = Dic₁₅⋊₅D₄	φ: C₁₂⋊₃D₄/C₂×C₃⋊D₄ → C₂ ⊆ Aut C₅	240		C5:3(C12:3D4)	480,643
C₅⋊₄(C₁₂⋊₃D₄) = C₆₀⋊₃D₄	φ: C₁₂⋊₃D₄/C₆×D₄ → C₂ ⊆ Aut C₅	240		C5:4(C12:3D4)	480,905

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁