Extensions 1→N→G→Q→1 with N=C₂₇ and Q=C₃×S₃

Direct product G=N×Q with N=C₂₇ and Q=C₃×S₃

		d	ρ	Label	ID
S₃×C₃×C₂₇		162		S3xC3xC27	486,112

Semidirect products G=N:Q with N=C₂₇ and Q=C₃×S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₇⋊(C₃×S₃) = C₃³.₅D₉	φ: C₃×S₃/C₃ → C₆ ⊆ Aut C₂₇	81		C27:(C3xS3)	486,162
C₂₇⋊₂(C₃×S₃) = S₃×C₂₇⋊C₃	φ: C₃×S₃/S₃ → C₃ ⊆ Aut C₂₇	54	6	C27:2(C3xS3)	486,114
C₂₇⋊₃(C₃×S₃) = C₃×C₂₇⋊S₃	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₂₇	162		C27:3(C3xS3)	486,160

Non-split extensions G=N.Q with N=C₂₇ and Q=C₃×S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₇.₁(C₃×S₃) = C₃×D₈₁	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₂₇	162	2	C27.1(C3xS3)	486,32
C₂₇.₂(C₃×S₃) = C₈₁⋊C₆	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₂₇	81	6+	C27.2(C3xS3)	486,34
C₂₇.₃(C₃×S₃) = He₃.₅D₉	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₂₇	81	6+	C27.3(C3xS3)	486,163
C₂₇.₄(C₃×S₃) = S₃×C₈₁	central extension (φ=1)	162	2	C27.4(C3xS3)	486,33

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