Extensions 1→N→G→Q→1 with N=C₅ and Q=C₆.D₄

Direct product G=N×Q with N=C₅ and Q=C₆.D₄

		d	ρ	Label	ID
C₅×C₆.D₄		120		C5xC6.D4	240,64

Semidirect products G=N:Q with N=C₅ and Q=C₆.D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₆.D₄) = D₁₀.D₆	φ: C₆.D₄/C₂×C₆ → C₄ ⊆ Aut C₅	60	4	C5:(C6.D4)	240,124
C₅⋊₂(C₆.D₄) = D₁₀⋊Dic₃	φ: C₆.D₄/C₂×Dic₃ → C₂ ⊆ Aut C₅	120		C5:2(C6.D4)	240,26
C₅⋊₃(C₆.D₄) = C₃₀.₃₈D₄	φ: C₆.D₄/C₂²×C₆ → C₂ ⊆ Aut C₅	120		C5:3(C6.D4)	240,80

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁