Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂²×He₃

Direct product G=N×Q with N=C₃ and Q=C₂²×He₃

		d	ρ	Label	ID
C₂×C₆×He₃		108		C2xC6xHe3	324,152

Semidirect products G=N:Q with N=C₃ and Q=C₂²×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₂²×He₃) = C₂×S₃×He₃	φ: C₂²×He₃/C₂×He₃ → C₂ ⊆ Aut C₃	36	6	C3:(C2^2xHe3)	324,139

Non-split extensions G=N.Q with N=C₃ and Q=C₂²×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₂²×He₃) = C₂²×C₃²⋊C₉	central extension (φ=1)	108		C3.1(C2^2xHe3)	324,82
C₃.₂(C₂²×He₃) = C₂²×C₃≀C₃	central stem extension (φ=1)	36		C3.2(C2^2xHe3)	324,86
C₃.₃(C₂²×He₃) = C₂²×He₃.C₃	central stem extension (φ=1)	108		C3.3(C2^2xHe3)	324,87
C₃.₄(C₂²×He₃) = C₂²×He₃⋊C₃	central stem extension (φ=1)	108		C3.4(C2^2xHe3)	324,88
C₃.₅(C₂²×He₃) = C₂²×C₃.He₃	central stem extension (φ=1)	108		C3.5(C2^2xHe3)	324,89

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁