Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₃⋊Dic₃

Direct product G=N×Q with N=C₁₀ and Q=C₃⋊Dic₃

		d	ρ	Label	ID
C₁₀×C₃⋊Dic₃		360		C10xC3:Dic3	360,108

Semidirect products G=N:Q with N=C₁₀ and Q=C₃⋊Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊(C₃⋊Dic₃) = C₂×C₃²⋊₃F₅	φ: C₃⋊Dic₃/C₃² → C₄ ⊆ Aut C₁₀	90		C10:(C3:Dic3)	360,147
C₁₀⋊₂(C₃⋊Dic₃) = C₂×C₃⋊Dic₁₅	φ: C₃⋊Dic₃/C₃×C₆ → C₂ ⊆ Aut C₁₀	360		C10:2(C3:Dic3)	360,113

Non-split extensions G=N.Q with N=C₁₀ and Q=C₃⋊Dic₃

extension	φ:Q→Aut N	d	Label	ID
C₁₀.(C₃⋊Dic₃) = C₃₀.Dic₃	φ: C₃⋊Dic₃/C₃² → C₄ ⊆ Aut C₁₀	360	C10.(C3:Dic3)	360,54
C₁₀.₂(C₃⋊Dic₃) = C₆₀.S₃	φ: C₃⋊Dic₃/C₃×C₆ → C₂ ⊆ Aut C₁₀	360	C10.2(C3:Dic3)	360,37
C₁₀.₃(C₃⋊Dic₃) = C₅×C₃²⋊₄C₈	central extension (φ=1)	360	C10.3(C3:Dic3)	360,36

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C10 and Q=C3⋊Dic3