Extensions 1→N→G→Q→1 with N=C₂² and Q=D₅×A₄

Direct product G=N×Q with N=C₂² and Q=D₅×A₄

		d	ρ	Label	ID
C₂²×D₅×A₄		60		C2^2xD5xA4	480,1202

Semidirect products G=N:Q with N=C₂² and Q=D₅×A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊(D₅×A₄) = D₅×C₂²⋊A₄	φ: D₅×A₄/C₂²×D₅ → C₃ ⊆ Aut C₂²	60		C2^2:(D5xA4)	480,1203
C₂²⋊₂(D₅×A₄) = A₄×C₅⋊D₄	φ: D₅×A₄/C₅×A₄ → C₂ ⊆ Aut C₂²	60	6	C2^2:2(D5xA4)	480,1045

Non-split extensions G=N.Q with N=C₂² and Q=D₅×A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².₁(D₅×A₄) = C₂₀⋊₄D₄⋊C₃	φ: D₅×A₄/C₂²×D₅ → C₃ ⊆ Aut C₂²	60	6+	C2^2.1(D5xA4)	480,262
C₂².₂(D₅×A₄) = (C₄×C₂₀)⋊C₆	φ: D₅×A₄/C₂²×D₅ → C₃ ⊆ Aut C₂²	80	6	C2^2.2(D5xA4)	480,263
C₂².₃(D₅×A₄) = D₅×C₄²⋊C₃	φ: D₅×A₄/C₂²×D₅ → C₃ ⊆ Aut C₂²	60	6	C2^2.3(D5xA4)	480,264
C₂².₄(D₅×A₄) = (C₂²×D₅)⋊A₄	φ: D₅×A₄/C₂²×D₅ → C₃ ⊆ Aut C₂²	40	6	C2^2.4(D5xA4)	480,268
C₂².₅(D₅×A₄) = SL₂(𝔽₃).₁₁D₁₀	φ: D₅×A₄/C₅×A₄ → C₂ ⊆ Aut C₂²	80	4	C2^2.5(D5xA4)	480,1040
C₂².₆(D₅×A₄) = Dic₅×SL₂(𝔽₃)	central extension (φ=1)	160		C2^2.6(D5xA4)	480,266
C₂².₇(D₅×A₄) = C₂×Dic₅.A₄	central extension (φ=1)	160		C2^2.7(D5xA4)	480,1038
C₂².₈(D₅×A₄) = C₂×D₅×SL₂(𝔽₃)	central extension (φ=1)	80		C2^2.8(D5xA4)	480,1039
C₂².₉(D₅×A₄) = C₂×A₄×Dic₅	central extension (φ=1)	120		C2^2.9(D5xA4)	480,1044

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁