Extensions 1→N→G→Q→1 with N=C₆ and Q=C₂×C₁₀

Direct product G=N×Q with N=C₆ and Q=C₂×C₁₀

		d	ρ	Label	ID
C₂²×C₃₀		120		C2^2xC30	120,47

Semidirect products G=N:Q with N=C₆ and Q=C₂×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊(C₂×C₁₀) = S₃×C₂×C₁₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₆	60		C6:(C2xC10)	120,45

Non-split extensions G=N.Q with N=C₆ and Q=C₂×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₂×C₁₀) = C₅×Dic₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₆	120	2	C6.1(C2xC10)	120,21
C₆.₂(C₂×C₁₀) = S₃×C₂₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₆	60	2	C6.2(C2xC10)	120,22
C₆.₃(C₂×C₁₀) = C₅×D₁₂	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₆	60	2	C6.3(C2xC10)	120,23
C₆.₄(C₂×C₁₀) = C₁₀×Dic₃	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₆	120		C6.4(C2xC10)	120,24
C₆.₅(C₂×C₁₀) = C₅×C₃⋊D₄	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₆	60	2	C6.5(C2xC10)	120,25
C₆.₆(C₂×C₁₀) = D₄×C₁₅	central extension (φ=1)	60	2	C6.6(C2xC10)	120,32
C₆.₇(C₂×C₁₀) = Q₈×C₁₅	central extension (φ=1)	120	2	C6.7(C2xC10)	120,33

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