Extensions 1→N→G→Q→1 with N=C₅ and Q=S₃×M₄(2)

Direct product G=N×Q with N=C₅ and Q=S₃×M₄(2)

		d	ρ	Label	ID
C₅×S₃×M₄(2)		120	4	C5xS3xM4(2)	480,785

Semidirect products G=N:Q with N=C₅ and Q=S₃×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(S₃×M₄(2)) = S₃×C₄.F₅	φ: S₃×M₄(2)/C₄×S₃ → C₄ ⊆ Aut C₅	120	8	C5:1(S3xM4(2))	480,988
C₅⋊₂(S₃×M₄(2)) = D₁₅⋊M₄(2)	φ: S₃×M₄(2)/C₄×S₃ → C₄ ⊆ Aut C₅	120	8	C5:2(S3xM4(2))	480,991
C₅⋊₃(S₃×M₄(2)) = D₁₅⋊₂M₄(2)	φ: S₃×M₄(2)/C₂×Dic₃ → C₄ ⊆ Aut C₅	120	8+	C5:3(S3xM4(2))	480,1007
C₅⋊₄(S₃×M₄(2)) = S₃×C₂².F₅	φ: S₃×M₄(2)/C₂²×S₃ → C₄ ⊆ Aut C₅	120	8-	C5:4(S3xM4(2))	480,1004
C₅⋊₅(S₃×M₄(2)) = S₃×C₈⋊D₅	φ: S₃×M₄(2)/S₃×C₈ → C₂ ⊆ Aut C₅	120	4	C5:5(S3xM4(2))	480,321
C₅⋊₆(S₃×M₄(2)) = C₄₀⋊D₆	φ: S₃×M₄(2)/C₈⋊S₃ → C₂ ⊆ Aut C₅	120	4	C5:6(S3xM4(2))	480,322
C₅⋊₇(S₃×M₄(2)) = D₁₅⋊₄M₄(2)	φ: S₃×M₄(2)/C₄.Dic₃ → C₂ ⊆ Aut C₅	120	4	C5:7(S3xM4(2))	480,368
C₅⋊₈(S₃×M₄(2)) = M₄(2)×D₁₅	φ: S₃×M₄(2)/C₃×M₄(2) → C₂ ⊆ Aut C₅	120	4	C5:8(S3xM4(2))	480,871
C₅⋊₉(S₃×M₄(2)) = S₃×C₄.Dic₅	φ: S₃×M₄(2)/S₃×C₂×C₄ → C₂ ⊆ Aut C₅	120	4	C5:9(S3xM4(2))	480,363

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁