Extensions 1→N→G→Q→1 with N=C₅ and Q=Q₁₆⋊S₃

Direct product G=N×Q with N=C₅ and Q=Q₁₆⋊S₃

		d	ρ	Label	ID
C₅×Q₁₆⋊S₃		240	4	C5xQ16:S3	480,797

Semidirect products G=N:Q with N=C₅ and Q=Q₁₆⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(Q₁₆⋊S₃) = Dic₂₀⋊S₃	φ: Q₁₆⋊S₃/C₈⋊S₃ → C₂ ⊆ Aut C₅	240	4	C5:1(Q16:S3)	480,339
C₅⋊₂(Q₁₆⋊S₃) = D₃₀.₄D₄	φ: Q₁₆⋊S₃/C₂₄⋊C₂ → C₂ ⊆ Aut C₅	240	4	C5:2(Q16:S3)	480,356
C₅⋊₃(Q₁₆⋊S₃) = D₃₀.₄₄D₄	φ: Q₁₆⋊S₃/Q₈⋊₂S₃ → C₂ ⊆ Aut C₅	240	8-	C5:3(Q16:S3)	480,600
C₅⋊₄(Q₁₆⋊S₃) = C₆₀.C₂³	φ: Q₁₆⋊S₃/C₃⋊Q₁₆ → C₂ ⊆ Aut C₅	240	8+	C5:4(Q16:S3)	480,588
C₅⋊₅(Q₁₆⋊S₃) = Q₁₆⋊D₁₅	φ: Q₁₆⋊S₃/C₃×Q₁₆ → C₂ ⊆ Aut C₅	240	4	C5:5(Q16:S3)	480,883
C₅⋊₆(Q₁₆⋊S₃) = C₆₀.₄₄C₂³	φ: Q₁₆⋊S₃/S₃×Q₈ → C₂ ⊆ Aut C₅	240	8+	C5:6(Q16:S3)	480,596
C₅⋊₇(Q₁₆⋊S₃) = Dic₁₀.₂₆D₆	φ: Q₁₆⋊S₃/Q₈⋊₃S₃ → C₂ ⊆ Aut C₅	240	8-	C5:7(Q16:S3)	480,586

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁