Extensions 1→N→G→Q→1 with N=Dic₅ and Q=C₂×A₄

Direct product G=N×Q with N=Dic₅ and Q=C₂×A₄

		d	ρ	Label	ID
C₂×A₄×Dic₅		120		C2xA4xDic5	480,1044

Semidirect products G=N:Q with N=Dic₅ and Q=C₂×A₄

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₅⋊(C₂×A₄) = A₄×C₅⋊D₄	φ: C₂×A₄/A₄ → C₂ ⊆ Out Dic₅	60	6	Dic5:(C2xA4)	480,1045
Dic₅⋊₂(C₂×A₄) = C₄×D₅×A₄	φ: trivial image	60	6	Dic5:2(C2xA4)	480,1036

Non-split extensions G=N.Q with N=Dic₅ and Q=C₂×A₄

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₅.₁(C₂×A₄) = A₄×Dic₁₀	φ: C₂×A₄/A₄ → C₂ ⊆ Out Dic₅	120	6-	Dic5.1(C2xA4)	480,1035
Dic₅.₂(C₂×A₄) = SL₂(𝔽₃).₁₁D₁₀	φ: C₂×A₄/A₄ → C₂ ⊆ Out Dic₅	80	4	Dic5.2(C2xA4)	480,1040
Dic₅.₃(C₂×A₄) = Dic₁₀.A₄	φ: C₂×A₄/A₄ → C₂ ⊆ Out Dic₅	120	4+	Dic5.3(C2xA4)	480,1041
Dic₅.₄(C₂×A₄) = SL₂(𝔽₃).F₅	φ: C₂×A₄/A₄ → C₂ ⊆ Out Dic₅	160	8+	Dic5.4(C2xA4)	480,964
Dic₅.₅(C₂×A₄) = A₄×C₅⋊C₈	φ: C₂×A₄/A₄ → C₂ ⊆ Out Dic₅	120	12-	Dic5.5(C2xA4)	480,966
Dic₅.₆(C₂×A₄) = C₂×Dic₅.A₄	φ: trivial image	160		Dic5.6(C2xA4)	480,1038
Dic₅.₇(C₂×A₄) = D₅×C₄.A₄	φ: trivial image	80	4	Dic5.7(C2xA4)	480,1042

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁