Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₃×Dic₅

Direct product G=N×Q with N=C₂³ and Q=C₃×Dic₅

		d	ρ	Label	ID
Dic₅×C₂²×C₆		480		Dic5xC2^2xC6	480,1148

Semidirect products G=N:Q with N=C₂³ and Q=C₃×Dic₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(C₃×Dic₅) = C₃×C₂³⋊Dic₅	φ: C₃×Dic₅/C₁₅ → C₄ ⊆ Aut C₂³	120	4	C2^3:(C3xDic5)	480,112
C₂³⋊₂(C₃×Dic₅) = C₂×A₄×Dic₅	φ: C₃×Dic₅/Dic₅ → C₃ ⊆ Aut C₂³	120		C2^3:2(C3xDic5)	480,1044
C₂³⋊₃(C₃×Dic₅) = C₆×C₂³.D₅	φ: C₃×Dic₅/C₃₀ → C₂ ⊆ Aut C₂³	240		C2^3:3(C3xDic5)	480,745

Non-split extensions G=N.Q with N=C₂³ and Q=C₃×Dic₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(C₃×Dic₅) = C₃×C₂₀.D₄	φ: C₃×Dic₅/C₁₅ → C₄ ⊆ Aut C₂³	120	4	C2^3.(C3xDic5)	480,111
C₂³.₂(C₃×Dic₅) = A₄×C₅⋊₂C₈	φ: C₃×Dic₅/Dic₅ → C₃ ⊆ Aut C₂³	120	6	C2^3.2(C3xDic5)	480,265
C₂³.₃(C₃×Dic₅) = C₃×C₂₀.₅₅D₄	φ: C₃×Dic₅/C₃₀ → C₂ ⊆ Aut C₂³	240		C2^3.3(C3xDic5)	480,108
C₂³.₄(C₃×Dic₅) = C₆×C₄.Dic₅	φ: C₃×Dic₅/C₃₀ → C₂ ⊆ Aut C₂³	240		C2^3.4(C3xDic5)	480,714
C₂³.₅(C₃×Dic₅) = C₂×C₆×C₅⋊₂C₈	central extension (φ=1)	480		C2^3.5(C3xDic5)	480,713

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁