Extensions 1→N→G→Q→1 with N=C₅ and Q=C₄²⋊₂S₃

Direct product G=N×Q with N=C₅ and Q=C₄²⋊₂S₃

		d	ρ	Label	ID
C₅×C₄²⋊₂S₃		240		C5xC4^2:2S3	480,751

Semidirect products G=N:Q with N=C₅ and Q=C₄²⋊₂S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₄²⋊₂S₃) = (C₄×S₃)⋊F₅	φ: C₄²⋊₂S₃/C₄×S₃ → C₄ ⊆ Aut C₅	120	8	C5:(C4^2:2S3)	480,985
C₅⋊₂(C₄²⋊₂S₃) = (C₄×D₁₅)⋊₁₀C₄	φ: C₄²⋊₂S₃/C₄×Dic₃ → C₂ ⊆ Aut C₅	240		C5:2(C4^2:2S3)	480,462
C₅⋊₃(C₄²⋊₂S₃) = D₃₀.C₂⋊C₄	φ: C₄²⋊₂S₃/Dic₃⋊C₄ → C₂ ⊆ Aut C₅	240		C5:3(C4^2:2S3)	480,478
C₅⋊₄(C₄²⋊₂S₃) = D₆.(C₄×D₅)	φ: C₄²⋊₂S₃/D₆⋊C₄ → C₂ ⊆ Aut C₅	240		C5:4(C4^2:2S3)	480,474
C₅⋊₅(C₄²⋊₂S₃) = C₄²⋊₂D₁₅	φ: C₄²⋊₂S₃/C₄×C₁₂ → C₂ ⊆ Aut C₅	240		C5:5(C4^2:2S3)	480,837
C₅⋊₆(C₄²⋊₂S₃) = (S₃×C₂₀)⋊₇C₄	φ: C₄²⋊₂S₃/S₃×C₂×C₄ → C₂ ⊆ Aut C₅	240		C5:6(C4^2:2S3)	480,447

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁