Extensions 1→N→G→Q→1 with N=C₃ and Q=C₅×He₃

Direct product G=N×Q with N=C₃ and Q=C₅×He₃

		d	ρ	Label	ID
C₁₅×He₃		135		C15xHe3	405,12

Non-split extensions G=N.Q with N=C₃ and Q=C₅×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₅×He₃) = C₅×C₃²⋊C₉	central extension (φ=1)	135		C3.1(C5xHe3)	405,3
C₃.₂(C₅×He₃) = C₅×C₃≀C₃	central stem extension (φ=1)	45	3	C3.2(C5xHe3)	405,7
C₃.₃(C₅×He₃) = C₅×He₃.C₃	central stem extension (φ=1)	135	3	C3.3(C5xHe3)	405,8
C₃.₄(C₅×He₃) = C₅×He₃⋊C₃	central stem extension (φ=1)	135	3	C3.4(C5xHe3)	405,9
C₃.₅(C₅×He₃) = C₅×C₃.He₃	central stem extension (φ=1)	135	3	C3.5(C5xHe3)	405,10

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁