Extensions 1→N→G→Q→1 with N=C₄ and Q=D₅×A₄

Direct product G=N×Q with N=C₄ and Q=D₅×A₄

		d	ρ	Label	ID
C₄×D₅×A₄		60	6	C4xD5xA4	480,1036

Semidirect products G=N:Q with N=C₄ and Q=D₅×A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(D₅×A₄) = A₄×D₂₀	φ: D₅×A₄/C₅×A₄ → C₂ ⊆ Aut C₄	60	6+	C4:(D5xA4)	480,1037

Non-split extensions G=N.Q with N=C₄ and Q=D₅×A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(D₅×A₄) = A₄×Dic₁₀	φ: D₅×A₄/C₅×A₄ → C₂ ⊆ Aut C₄	120	6-	C4.1(D5xA4)	480,1035
C₄.₂(D₅×A₄) = Dic₁₀.A₄	φ: D₅×A₄/C₅×A₄ → C₂ ⊆ Aut C₄	120	4+	C4.2(D5xA4)	480,1041
C₄.₃(D₅×A₄) = D₂₀.A₄	φ: D₅×A₄/C₅×A₄ → C₂ ⊆ Aut C₄	80	4-	C4.3(D5xA4)	480,1043
C₄.₄(D₅×A₄) = A₄×C₅⋊₂C₈	central extension (φ=1)	120	6	C4.4(D5xA4)	480,265
C₄.₅(D₅×A₄) = SL₂(𝔽₃).Dic₅	central extension (φ=1)	160	4	C4.5(D5xA4)	480,267
C₄.₆(D₅×A₄) = D₅×C₄.A₄	central extension (φ=1)	80	4	C4.6(D5xA4)	480,1042

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁