Extensions 1→N→G→Q→1 with N=C₆ and Q=C₂².F₅

Direct product G=N×Q with N=C₆ and Q=C₂².F₅

		d	ρ	Label	ID
C₆×C₂².F₅		240		C6xC2^2.F5	480,1058

Semidirect products G=N:Q with N=C₆ and Q=C₂².F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁(C₂².F₅) = C₂×D₆.F₅	φ: C₂².F₅/C₅⋊C₈ → C₂ ⊆ Aut C₆	240		C6:1(C2^2.F5)	480,1008
C₆⋊₂(C₂².F₅) = C₂×C₁₅⋊₈M₄(2)	φ: C₂².F₅/C₂×Dic₅ → C₂ ⊆ Aut C₆	240		C6:2(C2^2.F5)	480,1071

Non-split extensions G=N.Q with N=C₆ and Q=C₂².F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₂².F₅) = C₃₀.M₄(2)	φ: C₂².F₅/C₅⋊C₈ → C₂ ⊆ Aut C₆	480		C6.1(C2^2.F5)	480,245
C₆.₂(C₂².F₅) = Dic₅.₂₂D₁₂	φ: C₂².F₅/C₅⋊C₈ → C₂ ⊆ Aut C₆	240		C6.2(C2^2.F5)	480,246
C₆.₃(C₂².F₅) = Dic₁₅⋊C₈	φ: C₂².F₅/C₅⋊C₈ → C₂ ⊆ Aut C₆	480		C6.3(C2^2.F5)	480,253
C₆.₄(C₂².F₅) = C₃₀.₁₁C₄²	φ: C₂².F₅/C₂×Dic₅ → C₂ ⊆ Aut C₆	480		C6.4(C2^2.F5)	480,307
C₆.₅(C₂².F₅) = Dic₅.₁₃D₁₂	φ: C₂².F₅/C₂×Dic₅ → C₂ ⊆ Aut C₆	480		C6.5(C2^2.F5)	480,309
C₆.₆(C₂².F₅) = C₃₀.₂₂M₄(2)	φ: C₂².F₅/C₂×Dic₅ → C₂ ⊆ Aut C₆	240		C6.6(C2^2.F5)	480,317
C₆.₇(C₂².F₅) = C₃×C₁₀.C₄²	central extension (φ=1)	480		C6.7(C2^2.F5)	480,282
C₆.₈(C₂².F₅) = C₃×Dic₅⋊C₈	central extension (φ=1)	480		C6.8(C2^2.F5)	480,284
C₆.₉(C₂².F₅) = C₃×C₂³.₂F₅	central extension (φ=1)	240		C6.9(C2^2.F5)	480,292

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