Extensions 1→N→G→Q→1 with N=C₃ and Q=C₁₀.D₈

Direct product G=N×Q with N=C₃ and Q=C₁₀.D₈

		d	ρ	Label	ID
C₃×C₁₀.D₈		480		C3xC10.D8	480,85

Semidirect products G=N:Q with N=C₃ and Q=C₁₀.D₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₁₀.D₈) = C₆₀.₈Q₈	φ: C₁₀.D₈/C₂×C₅⋊₂C₈ → C₂ ⊆ Aut C₃	480		C3:1(C10.D8)	480,64
C₃⋊₂(C₁₀.D₈) = C₃₀.₂₀D₈	φ: C₁₀.D₈/C₄⋊Dic₅ → C₂ ⊆ Aut C₃	480		C3:2(C10.D8)	480,65
C₃⋊₃(C₁₀.D₈) = C₆₀.₁Q₈	φ: C₁₀.D₈/C₅×C₄⋊C₄ → C₂ ⊆ Aut C₃	480		C3:3(C10.D8)	480,167

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁