Extensions 1→N→G→Q→1 with N=C₆ and Q=C₅×D₈

Direct product G=N×Q with N=C₆ and Q=C₅×D₈

		d	ρ	Label	ID
D₈×C₃₀		240		D8xC30	480,937

Semidirect products G=N:Q with N=C₆ and Q=C₅×D₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁(C₅×D₈) = C₁₀×D₂₄	φ: C₅×D₈/C₄₀ → C₂ ⊆ Aut C₆	240		C6:1(C5xD8)	480,782
C₆⋊₂(C₅×D₈) = C₁₀×D₄⋊S₃	φ: C₅×D₈/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6:2(C5xD8)	480,810

Non-split extensions G=N.Q with N=C₆ and Q=C₅×D₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₅×D₈) = C₅×D₄₈	φ: C₅×D₈/C₄₀ → C₂ ⊆ Aut C₆	240	2	C6.1(C5xD8)	480,118
C₆.₂(C₅×D₈) = C₅×C₄₈⋊C₂	φ: C₅×D₈/C₄₀ → C₂ ⊆ Aut C₆	240	2	C6.2(C5xD8)	480,119
C₆.₃(C₅×D₈) = C₅×Dic₂₄	φ: C₅×D₈/C₄₀ → C₂ ⊆ Aut C₆	480	2	C6.3(C5xD8)	480,120
C₆.₄(C₅×D₈) = C₅×C₂₄⋊₁C₄	φ: C₅×D₈/C₄₀ → C₂ ⊆ Aut C₆	480		C6.4(C5xD8)	480,137
C₆.₅(C₅×D₈) = C₅×C₂.D₂₄	φ: C₅×D₈/C₄₀ → C₂ ⊆ Aut C₆	240		C6.5(C5xD8)	480,140
C₆.₆(C₅×D₈) = C₅×C₆.Q₁₆	φ: C₅×D₈/C₅×D₄ → C₂ ⊆ Aut C₆	480		C6.6(C5xD8)	480,126
C₆.₇(C₅×D₈) = C₅×C₆.D₈	φ: C₅×D₈/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6.7(C5xD8)	480,128
C₆.₈(C₅×D₈) = C₅×C₃⋊D₁₆	φ: C₅×D₈/C₅×D₄ → C₂ ⊆ Aut C₆	240	4	C6.8(C5xD8)	480,145
C₆.₉(C₅×D₈) = C₅×D₈.S₃	φ: C₅×D₈/C₅×D₄ → C₂ ⊆ Aut C₆	240	4	C6.9(C5xD8)	480,146
C₆.₁₀(C₅×D₈) = C₅×C₈.₆D₆	φ: C₅×D₈/C₅×D₄ → C₂ ⊆ Aut C₆	240	4	C6.10(C5xD8)	480,147
C₆.₁₁(C₅×D₈) = C₅×C₃⋊Q₃₂	φ: C₅×D₈/C₅×D₄ → C₂ ⊆ Aut C₆	480	4	C6.11(C5xD8)	480,148
C₆.₁₂(C₅×D₈) = C₅×D₄⋊Dic₃	φ: C₅×D₈/C₅×D₄ → C₂ ⊆ Aut C₆	240		C6.12(C5xD8)	480,151
C₆.₁₃(C₅×D₈) = C₁₅×D₄⋊C₄	central extension (φ=1)	240		C6.13(C5xD8)	480,205
C₆.₁₄(C₅×D₈) = C₁₅×C₂.D₈	central extension (φ=1)	480		C6.14(C5xD8)	480,210
C₆.₁₅(C₅×D₈) = C₁₅×D₁₆	central extension (φ=1)	240	2	C6.15(C5xD8)	480,214
C₆.₁₆(C₅×D₈) = C₁₅×SD₃₂	central extension (φ=1)	240	2	C6.16(C5xD8)	480,215
C₆.₁₇(C₅×D₈) = C₁₅×Q₃₂	central extension (φ=1)	480	2	C6.17(C5xD8)	480,216

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁