Extensions 1→N→G→Q→1 with N=C₃ and Q=He₃.₄S₃

Direct product G=N×Q with N=C₃ and Q=He₃.₄S₃

		d	ρ	Label	ID
C₃×He₃.₄S₃		54	6	C3xHe3.4S3	486,234

Semidirect products G=N:Q with N=C₃ and Q=He₃.₄S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(He₃.₄S₃) = C₉○He₃⋊₃S₃	φ: He₃.₄S₃/C₉○He₃ → C₂ ⊆ Aut C₃	81		C3:(He3.4S3)	486,245

Non-split extensions G=N.Q with N=C₃ and Q=He₃.₄S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(He₃.₄S₃) = C₉²⋊₃C₆	φ: He₃.₄S₃/C₉○He₃ → C₂ ⊆ Aut C₃	81		C3.1(He3.4S3)	486,141
C₃.₂(He₃.₄S₃) = He₃⋊₃D₉	φ: He₃.₄S₃/C₉○He₃ → C₂ ⊆ Aut C₃	81		C3.2(He3.4S3)	486,142
C₃.₃(He₃.₄S₃) = C₉²⋊₉C₆	φ: He₃.₄S₃/C₉○He₃ → C₂ ⊆ Aut C₃	81		C3.3(He3.4S3)	486,144
C₃.₄(He₃.₄S₃) = C₉⋊He₃⋊₂C₂	φ: He₃.₄S₃/C₉○He₃ → C₂ ⊆ Aut C₃	81		C3.4(He3.4S3)	486,148
C₃.₅(He₃.₄S₃) = (C₃²×C₉)⋊C₆	φ: He₃.₄S₃/C₉○He₃ → C₂ ⊆ Aut C₃	81		C3.5(He3.4S3)	486,151
C₃.₆(He₃.₄S₃) = C₉²⋊₁₀C₆	φ: He₃.₄S₃/C₉○He₃ → C₂ ⊆ Aut C₃	81		C3.6(He3.4S3)	486,154
C₃.₇(He₃.₄S₃) = C₉²⋊₄C₆	φ: He₃.₄S₃/C₉○He₃ → C₂ ⊆ Aut C₃	81		C3.7(He3.4S3)	486,155
C₃.₈(He₃.₄S₃) = C₉²⋊₅C₆	φ: He₃.₄S₃/C₉○He₃ → C₂ ⊆ Aut C₃	81		C3.8(He3.4S3)	486,157
C₃.₉(He₃.₄S₃) = C₉²⋊₁₁C₆	φ: He₃.₄S₃/C₉○He₃ → C₂ ⊆ Aut C₃	81		C3.9(He3.4S3)	486,158
C₃.₁₀(He₃.₄S₃) = C₉²⋊₃S₃	central extension (φ=1)	54	6	C3.10(He3.4S3)	486,139
C₃.₁₁(He₃.₄S₃) = (C₃²×C₉)⋊S₃	central stem extension (φ=1)	54	6	C3.11(He3.4S3)	486,149
C₃.₁₂(He₃.₄S₃) = C₉²⋊₆S₃	central stem extension (φ=1)	18	6	C3.12(He3.4S3)	486,153
C₃.₁₃(He₃.₄S₃) = C₉²⋊₅S₃	central stem extension (φ=1)	54	6	C3.13(He3.4S3)	486,156

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁