Extensions 1→N→G→Q→1 with N=C₃ and Q=C₁₂.₅₈D₆

Direct product G=N×Q with N=C₃ and Q=C₁₂.₅₈D₆

		d	ρ	Label	ID
C₃×C₁₂.₅₈D₆		72		C3xC12.58D6	432,486

Semidirect products G=N:Q with N=C₃ and Q=C₁₂.₅₈D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₁₂.₅₈D₆) = C₃³⋊₇M₄(2)	φ: C₁₂.₅₈D₆/C₃²⋊₄C₈ → C₂ ⊆ Aut C₃	144		C3:1(C12.58D6)	432,433
C₃⋊₂(C₁₂.₅₈D₆) = C₃³⋊₁₈M₄(2)	φ: C₁₂.₅₈D₆/C₆×C₁₂ → C₂ ⊆ Aut C₃	216		C3:2(C12.58D6)	432,502

Non-split extensions G=N.Q with N=C₃ and Q=C₁₂.₅₈D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₁₂.₅₈D₆) = C₃₆.₆₉D₆	φ: C₁₂.₅₈D₆/C₆×C₁₂ → C₂ ⊆ Aut C₃	216		C3.(C12.58D6)	432,179
C₃.₂(C₁₂.₅₈D₆) = He₃⋊₈M₄(2)	central stem extension (φ=1)	72	6	C3.2(C12.58D6)	432,185

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Extensions 1→N→G→Q→1 with N=C3 and Q=C12.58D6