Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂×He₃

Direct product G=N×Q with N=C₃ and Q=C₂×He₃

		d	ρ	Label	ID
C₆×He₃		54		C6xHe3	162,48

Semidirect products G=N:Q with N=C₃ and Q=C₂×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₂×He₃) = S₃×He₃	φ: C₂×He₃/He₃ → C₂ ⊆ Aut C₃	18	6	C3:(C2xHe3)	162,35

Non-split extensions G=N.Q with N=C₃ and Q=C₂×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₂×He₃) = C₂×C₃²⋊C₉	central extension (φ=1)	54		C3.1(C2xHe3)	162,24
C₃.₂(C₂×He₃) = C₂×C₃≀C₃	central stem extension (φ=1)	18	3	C3.2(C2xHe3)	162,28
C₃.₃(C₂×He₃) = C₂×He₃.C₃	central stem extension (φ=1)	54	3	C3.3(C2xHe3)	162,29
C₃.₄(C₂×He₃) = C₂×He₃⋊C₃	central stem extension (φ=1)	54	3	C3.4(C2xHe3)	162,30
C₃.₅(C₂×He₃) = C₂×C₃.He₃	central stem extension (φ=1)	54	3	C3.5(C2xHe3)	162,31

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁