Extensions 1→N→G→Q→1 with N=C₄ and Q=C₆²

Direct product G=N×Q with N=C₄ and Q=C₆²

		d	ρ	Label	ID
C₂×C₆×C₁₂		144		C2xC6xC12	144,178

Semidirect products G=N:Q with N=C₄ and Q=C₆²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊C₆² = D₄×C₃×C₆	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₄	72		C4:C6^2	144,179

Non-split extensions G=N.Q with N=C₄ and Q=C₆²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁C₆² = C₃²×D₈	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₄	72		C4.1C6^2	144,106
C₄.₂C₆² = C₃²×SD₁₆	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₄	72		C4.2C6^2	144,107
C₄.₃C₆² = C₃²×Q₁₆	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₄	144		C4.3C6^2	144,108
C₄.₄C₆² = Q₈×C₃×C₆	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₄	144		C4.4C6^2	144,180
C₄.₅C₆² = C₃²×C₄○D₄	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₄	72		C4.5C6^2	144,181
C₄.₆C₆² = C₃²×M₄(2)	central extension (φ=1)	72		C4.6C6^2	144,105

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁