Extensions 1→N→G→Q→1 with N=C₆ and Q=C₂×He₃

Direct product G=N×Q with N=C₆ and Q=C₂×He₃

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

Semidirect products G=N:Q with N=C₆ and Q=C₂×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊(C₂×He₃) = C₂×S₃×He₃	φ: C₂×He₃/He₃ → C₂ ⊆ Aut C₆	36	6	C6:(C2xHe3)	324,139

Non-split extensions G=N.Q with N=C₆ and Q=C₂×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.(C₂×He₃) = Dic₃×He₃	φ: C₂×He₃/He₃ → C₂ ⊆ Aut C₆	36	6	C6.(C2xHe3)	324,93
C₆.₂(C₂×He₃) = C₄×C₃²⋊C₉	central extension (φ=1)	108		C6.2(C2xHe3)	324,27
C₆.₃(C₂×He₃) = C₄×C₃≀C₃	central extension (φ=1)	36	3	C6.3(C2xHe3)	324,31
C₆.₄(C₂×He₃) = C₄×He₃.C₃	central extension (φ=1)	108	3	C6.4(C2xHe3)	324,32
C₆.₅(C₂×He₃) = C₄×He₃⋊C₃	central extension (φ=1)	108	3	C6.5(C2xHe3)	324,33
C₆.₆(C₂×He₃) = C₄×C₃.He₃	central extension (φ=1)	108	3	C6.6(C2xHe3)	324,34
C₆.₇(C₂×He₃) = C₂²×C₃²⋊C₉	central extension (φ=1)	108		C6.7(C2xHe3)	324,82
C₆.₈(C₂×He₃) = C₂²×C₃≀C₃	central extension (φ=1)	36		C6.8(C2xHe3)	324,86
C₆.₉(C₂×He₃) = C₂²×He₃.C₃	central extension (φ=1)	108		C6.9(C2xHe3)	324,87
C₆.₁₀(C₂×He₃) = C₂²×He₃⋊C₃	central extension (φ=1)	108		C6.10(C2xHe3)	324,88
C₆.₁₁(C₂×He₃) = C₂²×C₃.He₃	central extension (φ=1)	108		C6.11(C2xHe3)	324,89
C₆.₁₂(C₂×He₃) = C₁₂×He₃	central extension (φ=1)	108		C6.12(C2xHe3)	324,106

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁