Extensions 1→N→G→Q→1 with N=C₃⋊C₈ and Q=F₅

Direct product G=N×Q with N=C₃⋊C₈ and Q=F₅

		d	ρ	Label	ID
F₅×C₃⋊C₈		120	8	F5xC3:C8	480,223

Semidirect products G=N:Q with N=C₃⋊C₈ and Q=F₅

extension	φ:Q→Out N	d	ρ	Label	ID
C₃⋊C₈⋊₁F₅ = Dic₅.Dic₆	φ: F₅/D₅ → C₂ ⊆ Out C₃⋊C₈	120	8	C3:C8:1F5	480,235
C₃⋊C₈⋊₂F₅ = Dic₅.₄Dic₆	φ: F₅/D₅ → C₂ ⊆ Out C₃⋊C₈	120	8	C3:C8:2F5	480,236
C₃⋊C₈⋊₃F₅ = C₃₀.₃C₄²	φ: F₅/D₅ → C₂ ⊆ Out C₃⋊C₈	120	8	C3:C8:3F5	480,225
C₃⋊C₈⋊₄F₅ = C₃₀.₄C₄²	φ: F₅/D₅ → C₂ ⊆ Out C₃⋊C₈	120	8	C3:C8:4F5	480,226
C₃⋊C₈⋊₅F₅ = C₃₀.C₄²	φ: trivial image	120	8	C3:C8:5F5	480,224

Non-split extensions G=N.Q with N=C₃⋊C₈ and Q=F₅

extension	φ:Q→Out N	d	ρ	Label	ID
C₃⋊C₈.₁F₅ = D₁₀.Dic₆	φ: F₅/D₅ → C₂ ⊆ Out C₃⋊C₈	240	8	C3:C8.1F5	480,237
C₃⋊C₈.₂F₅ = D₁₀.₂Dic₆	φ: F₅/D₅ → C₂ ⊆ Out C₃⋊C₈	240	8	C3:C8.2F5	480,238
C₃⋊C₈.₃F₅ = D₃₀.C₈	φ: F₅/D₅ → C₂ ⊆ Out C₃⋊C₈	240	8	C3:C8.3F5	480,242
C₃⋊C₈.₄F₅ = D₁₅⋊C₁₆	φ: trivial image	240	8	C3:C8.4F5	480,240

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁