Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₅×Dic₃

Direct product G=N×Q with N=C₂³ and Q=C₅×Dic₃

		d	ρ	Label	ID
Dic₃×C₂²×C₁₀		480		Dic3xC2^2xC10	480,1163

Semidirect products G=N:Q with N=C₂³ and Q=C₅×Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(C₅×Dic₃) = C₁₀×A₄⋊C₄	φ: C₅×Dic₃/C₁₀ → S₃ ⊆ Aut C₂³	120		C2^3:(C5xDic3)	480,1022
C₂³⋊₂(C₅×Dic₃) = C₅×C₂³.₇D₆	φ: C₅×Dic₃/C₁₅ → C₄ ⊆ Aut C₂³	120	4	C2^3:2(C5xDic3)	480,153
C₂³⋊₃(C₅×Dic₃) = C₁₀×C₆.D₄	φ: C₅×Dic₃/C₃₀ → C₂ ⊆ Aut C₂³	240		C2^3:3(C5xDic3)	480,831

Non-split extensions G=N.Q with N=C₂³ and Q=C₅×Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(C₅×Dic₃) = C₅×A₄⋊C₈	φ: C₅×Dic₃/C₁₀ → S₃ ⊆ Aut C₂³	120	3	C2^3.(C5xDic3)	480,255
C₂³.₂(C₅×Dic₃) = C₅×C₁₂.D₄	φ: C₅×Dic₃/C₁₅ → C₄ ⊆ Aut C₂³	120	4	C2^3.2(C5xDic3)	480,152
C₂³.₃(C₅×Dic₃) = C₅×C₁₂.₅₅D₄	φ: C₅×Dic₃/C₃₀ → C₂ ⊆ Aut C₂³	240		C2^3.3(C5xDic3)	480,149
C₂³.₄(C₅×Dic₃) = C₁₀×C₄.Dic₃	φ: C₅×Dic₃/C₃₀ → C₂ ⊆ Aut C₂³	240		C2^3.4(C5xDic3)	480,800
C₂³.₅(C₅×Dic₃) = C₂×C₁₀×C₃⋊C₈	central extension (φ=1)	480		C2^3.5(C5xDic3)	480,799

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁