Extensions 1→N→G→Q→1 with N=C₇ and Q=C₂×He₃

Direct product G=N×Q with N=C₇ and Q=C₂×He₃

		d	ρ	Label	ID
C₁₄×He₃		126	3	C14xHe3	378,45

Semidirect products G=N:Q with N=C₇ and Q=C₂×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇⋊(C₂×He₃) = D₇⋊He₃	φ: C₂×He₃/C₃² → C₆ ⊆ Aut C₇	63	6	C7:(C2xHe3)	378,12
C₇⋊₂(C₂×He₃) = C₂×C₇⋊He₃	φ: C₂×He₃/C₃×C₆ → C₃ ⊆ Aut C₇	126	3	C7:2(C2xHe3)	378,28
C₇⋊₃(C₂×He₃) = D₇×He₃	φ: C₂×He₃/He₃ → C₂ ⊆ Aut C₇	63	6	C7:3(C2xHe3)	378,30

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁