Extensions 1→N→G→Q→1 with N=C₂₄ and Q=C₆

Direct product G=N×Q with N=C₂₄ and Q=C₆

		d	ρ	Label	ID
C₆×C₂₄		144		C6xC24	144,104

Semidirect products G=N:Q with N=C₂₄ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₄⋊₁C₆ = C₃×D₂₄	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	48	2	C24:1C6	144,72
C₂₄⋊₂C₆ = C₃×C₂₄⋊C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	48	2	C24:2C6	144,71
C₂₄⋊₃C₆ = C₃²×D₈	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	72		C24:3C6	144,106
C₂₄⋊₄C₆ = S₃×C₂₄	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	48	2	C24:4C6	144,69
C₂₄⋊₅C₆ = C₃×C₈⋊S₃	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	48	2	C24:5C6	144,70
C₂₄⋊₆C₆ = C₃²×SD₁₆	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	72		C24:6C6	144,107
C₂₄⋊₇C₆ = C₃²×M₄(2)	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	72		C24:7C6	144,105

Non-split extensions G=N.Q with N=C₂₄ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₄.₁C₆ = C₃×Dic₁₂	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	48	2	C24.1C6	144,73
C₂₄.₂C₆ = C₉×D₈	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	72	2	C24.2C6	144,25
C₂₄.₃C₆ = C₉×Q₁₆	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	144	2	C24.3C6	144,27
C₂₄.₄C₆ = C₃²×Q₁₆	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	144		C24.4C6	144,108
C₂₄.₅C₆ = C₃×C₃⋊C₁₆	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	48	2	C24.5C6	144,28
C₂₄.₆C₆ = C₉×SD₁₆	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	72	2	C24.6C6	144,26
C₂₄.₇C₆ = C₉×M₄(2)	φ: C₆/C₃ → C₂ ⊆ Aut C₂₄	72	2	C24.7C6	144,24

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁