Extensions 1→N→G→Q→1 with N=C₇ and Q=C₃×F₅

Direct product G=N×Q with N=C₇ and Q=C₃×F₅

		d	ρ	Label	ID
F₅×C₂₁		105	4	F5xC21	420,20

Semidirect products G=N:Q with N=C₇ and Q=C₃×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇⋊(C₃×F₅) = C₃₅⋊C₁₂	φ: C₃×F₅/D₅ → C₆ ⊆ Aut C₇	35	12	C7:(C3xF5)	420,15
C₇⋊₂(C₃×F₅) = F₅×C₇⋊C₃	φ: C₃×F₅/F₅ → C₃ ⊆ Aut C₇	35	12	C7:2(C3xF5)	420,14
C₇⋊₃(C₃×F₅) = C₃×C₇⋊F₅	φ: C₃×F₅/C₃×D₅ → C₂ ⊆ Aut C₇	105	4	C7:3(C3xF5)	420,21

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁