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

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

		d	ρ	Label	ID
C₃²×He₃		81		C3^2xHe3	243,62

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×He₃) = C₃×C₃²⋊C₉	central extension (φ=1)	81		C3.1(C3xHe3)	243,32
C₃.₂(C₃×He₃) = C₉×He₃	central extension (φ=1)	81		C3.2(C3xHe3)	243,35
C₃.₃(C₃×He₃) = C₃²⋊He₃	central stem extension (φ=1)	27		C3.3(C3xHe3)	243,37
C₃.₄(C₃×He₃) = C₃⁴.C₃	central stem extension (φ=1)	27		C3.4(C3xHe3)	243,38
C₃.₅(C₃×He₃) = C₉⋊He₃	central stem extension (φ=1)	81		C3.5(C3xHe3)	243,39
C₃.₆(C₃×He₃) = C₃².₂₃C₃³	central stem extension (φ=1)	81		C3.6(C3xHe3)	243,40
C₃.₇(C₃×He₃) = C₃×C₃≀C₃	central stem extension (φ=1)	27		C3.7(C3xHe3)	243,51
C₃.₈(C₃×He₃) = C₃×He₃.C₃	central stem extension (φ=1)	81		C3.8(C3xHe3)	243,52
C₃.₉(C₃×He₃) = C₃×He₃⋊C₃	central stem extension (φ=1)	81		C3.9(C3xHe3)	243,53
C₃.₁₀(C₃×He₃) = C₃×C₃.He₃	central stem extension (φ=1)	81		C3.10(C3xHe3)	243,54
C₃.₁₁(C₃×He₃) = C₉.He₃	central stem extension (φ=1)	27	3	C3.11(C3xHe3)	243,55
C₃.₁₂(C₃×He₃) = C₃³⋊C₃²	central stem extension (φ=1)	27	9	C3.12(C3xHe3)	243,56
C₃.₁₃(C₃×He₃) = He₃.C₃²	central stem extension (φ=1)	27	9	C3.13(C3xHe3)	243,57
C₃.₁₄(C₃×He₃) = He₃⋊C₃²	central stem extension (φ=1)	27	9	C3.14(C3xHe3)	243,58
C₃.₁₅(C₃×He₃) = C₃².C₃³	central stem extension (φ=1)	27	9	C3.15(C3xHe3)	243,59
C₃.₁₆(C₃×He₃) = C₉.₂He₃	central stem extension (φ=1)	27	9	C3.16(C3xHe3)	243,60

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