Extensions 1→N→G→Q→1 with N=C₆ and Q=D₂₀

Direct product G=N×Q with N=C₆ and Q=D₂₀

		d	ρ	Label	ID
C₆×D₂₀		120		C6xD20	240,157

Semidirect products G=N:Q with N=C₆ and Q=D₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁D₂₀ = C₂×D₆₀	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₆	120		C6:1D20	240,177
C₆⋊₂D₂₀ = C₂×C₃⋊D₂₀	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₆	120		C6:2D20	240,146

Non-split extensions G=N.Q with N=C₆ and Q=D₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁D₂₀ = C₂₄⋊D₅	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₆	120	2	C6.1D20	240,67
C₆.₂D₂₀ = D₁₂₀	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₆	120	2+	C6.2D20	240,68
C₆.₃D₂₀ = Dic₆₀	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₆	240	2-	C6.3D20	240,69
C₆.₄D₂₀ = C₆₀⋊₅C₄	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₆	240		C6.4D20	240,74
C₆.₅D₂₀ = D₃₀⋊₃C₄	φ: D₂₀/C₂₀ → C₂ ⊆ Aut C₆	120		C6.5D20	240,75
C₆.₆D₂₀ = C₃⋊D₄₀	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₆	120	4+	C6.6D20	240,14
C₆.₇D₂₀ = C₆.D₂₀	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₆	120	4-	C6.7D20	240,18
C₆.₈D₂₀ = C₁₅⋊SD₁₆	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₆	120	4+	C6.8D20	240,19
C₆.₉D₂₀ = C₃⋊Dic₂₀	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₆	240	4-	C6.9D20	240,23
C₆.₁₀D₂₀ = D₁₀⋊Dic₃	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₆	120		C6.10D20	240,26
C₆.₁₁D₂₀ = D₃₀⋊₄C₄	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₆	120		C6.11D20	240,28
C₆.₁₂D₂₀ = C₆.Dic₁₀	φ: D₂₀/D₁₀ → C₂ ⊆ Aut C₆	240		C6.12D20	240,31
C₆.₁₃D₂₀ = C₃×C₄₀⋊C₂	central extension (φ=1)	120	2	C6.13D20	240,35
C₆.₁₄D₂₀ = C₃×D₄₀	central extension (φ=1)	120	2	C6.14D20	240,36
C₆.₁₅D₂₀ = C₃×Dic₂₀	central extension (φ=1)	240	2	C6.15D20	240,37
C₆.₁₆D₂₀ = C₃×C₄⋊Dic₅	central extension (φ=1)	240		C6.16D20	240,42
C₆.₁₇D₂₀ = C₃×D₁₀⋊C₄	central extension (φ=1)	120		C6.17D20	240,43

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁