Extensions 1→N→G→Q→1 with N=C₃ and Q=C₅×C₃⋊S₃

Direct product G=N×Q with N=C₃ and Q=C₅×C₃⋊S₃

		d	ρ	Label	ID
C₁₅×C₃⋊S₃		90		C15xC3:S3	270,26

Semidirect products G=N:Q with N=C₃ and Q=C₅×C₃⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₅×C₃⋊S₃) = C₅×C₃³⋊C₂	φ: C₅×C₃⋊S₃/C₃×C₁₅ → C₂ ⊆ Aut C₃	135		C3:(C5xC3:S3)	270,28

Non-split extensions G=N.Q with N=C₃ and Q=C₅×C₃⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₅×C₃⋊S₃) = C₅×C₉⋊S₃	φ: C₅×C₃⋊S₃/C₃×C₁₅ → C₂ ⊆ Aut C₃	135		C3.(C5xC3:S3)	270,16
C₃.₂(C₅×C₃⋊S₃) = C₅×He₃⋊C₂	central stem extension (φ=1)	45	3	C3.2(C5xC3:S3)	270,17

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Extensions 1→N→G→Q→1 with N=C3 and Q=C5×C3⋊S3