Extensions 1→N→G→Q→1 with N=C₄ and Q=C₅×Dic₆

Direct product G=N×Q with N=C₄ and Q=C₅×Dic₆

		d	ρ	Label	ID
C₂₀×Dic₆		480		C20xDic6	480,747

Semidirect products G=N:Q with N=C₄ and Q=C₅×Dic₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₅×Dic₆) = C₅×C₁₂⋊Q₈	φ: C₅×Dic₆/C₅×Dic₃ → C₂ ⊆ Aut C₄	480		C4:1(C5xDic6)	480,767
C₄⋊₂(C₅×Dic₆) = C₅×C₁₂⋊₂Q₈	φ: C₅×Dic₆/C₆₀ → C₂ ⊆ Aut C₄	480		C4:2(C5xDic6)	480,748

Non-split extensions G=N.Q with N=C₄ and Q=C₅×Dic₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₅×Dic₆) = C₅×C₆.Q₁₆	φ: C₅×Dic₆/C₅×Dic₃ → C₂ ⊆ Aut C₄	480		C4.1(C5xDic6)	480,126
C₄.₂(C₅×Dic₆) = C₅×C₁₂.Q₈	φ: C₅×Dic₆/C₅×Dic₃ → C₂ ⊆ Aut C₄	480		C4.2(C5xDic6)	480,127
C₄.₃(C₅×Dic₆) = C₅×C₄.Dic₆	φ: C₅×Dic₆/C₅×Dic₃ → C₂ ⊆ Aut C₄	480		C4.3(C5xDic6)	480,769
C₄.₄(C₅×Dic₆) = C₅×C₈⋊Dic₃	φ: C₅×Dic₆/C₆₀ → C₂ ⊆ Aut C₄	480		C4.4(C5xDic6)	480,136
C₄.₅(C₅×Dic₆) = C₅×C₂₄⋊₁C₄	φ: C₅×Dic₆/C₆₀ → C₂ ⊆ Aut C₄	480		C4.5(C5xDic6)	480,137
C₄.₆(C₅×Dic₆) = C₅×C₁₂.₆Q₈	φ: C₅×Dic₆/C₆₀ → C₂ ⊆ Aut C₄	480		C4.6(C5xDic6)	480,749
C₄.₇(C₅×Dic₆) = C₅×C₁₂⋊C₈	central extension (φ=1)	480		C4.7(C5xDic6)	480,123
C₄.₈(C₅×Dic₆) = C₅×Dic₃⋊C₈	central extension (φ=1)	480		C4.8(C5xDic6)	480,133

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁