Extensions 1→N→G→Q→1 with N=C₆ and Q=C₅⋊D₅

Direct product G=N×Q with N=C₆ and Q=C₅⋊D₅

		d	ρ	Label	ID
C₆×C₅⋊D₅		150		C6xC5:D5	300,45

Semidirect products G=N:Q with N=C₆ and Q=C₅⋊D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊(C₅⋊D₅) = C₂×C₅⋊D₁₅	φ: C₅⋊D₅/C₅² → C₂ ⊆ Aut C₆	150		C6:(C5:D5)	300,48

Non-split extensions G=N.Q with N=C₆ and Q=C₅⋊D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.(C₅⋊D₅) = C₃₀.D₅	φ: C₅⋊D₅/C₅² → C₂ ⊆ Aut C₆	300		C6.(C5:D5)	300,20
C₆.₂(C₅⋊D₅) = C₃×C₅²⋊₆C₄	central extension (φ=1)	300		C6.2(C5:D5)	300,17

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C6 and Q=C5⋊D5