Extensions 1→N→G→Q→1 with N=C₂² and Q=C₅×Dic₆

Direct product G=N×Q with N=C₂² and Q=C₅×Dic₆

		d	ρ	Label	ID
C₂×C₁₀×Dic₆		480		C2xC10xDic6	480,1150

Semidirect products G=N:Q with N=C₂² and Q=C₅×Dic₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊(C₅×Dic₆) = C₅×A₄⋊Q₈	φ: C₅×Dic₆/C₂₀ → S₃ ⊆ Aut C₂²	120	6	C2^2:(C5xDic6)	480,1013
C₂²⋊₂(C₅×Dic₆) = C₅×Dic₃.D₄	φ: C₅×Dic₆/C₅×Dic₃ → C₂ ⊆ Aut C₂²	240		C2^2:2(C5xDic6)	480,757
C₂²⋊₃(C₅×Dic₆) = C₅×C₁₂.₄₈D₄	φ: C₅×Dic₆/C₆₀ → C₂ ⊆ Aut C₂²	240		C2^2:3(C5xDic6)	480,803

Non-split extensions G=N.Q with N=C₂² and Q=C₅×Dic₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².₁(C₅×Dic₆) = C₅×C₁₂.₅₃D₄	φ: C₅×Dic₆/C₅×Dic₃ → C₂ ⊆ Aut C₂²	240	4	C2^2.1(C5xDic6)	480,141
C₂².₂(C₅×Dic₆) = C₅×C₂₄.C₄	φ: C₅×Dic₆/C₆₀ → C₂ ⊆ Aut C₂²	240	2	C2^2.2(C5xDic6)	480,138
C₂².₃(C₅×Dic₆) = C₅×C₆.C₄²	central extension (φ=1)	480		C2^2.3(C5xDic6)	480,150
C₂².₄(C₅×Dic₆) = C₁₀×Dic₃⋊C₄	central extension (φ=1)	480		C2^2.4(C5xDic6)	480,802
C₂².₅(C₅×Dic₆) = C₁₀×C₄⋊Dic₃	central extension (φ=1)	480		C2^2.5(C5xDic6)	480,804

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁