Extensions 1→N→G→Q→1 with N=C₆₈ and Q=C₄

Direct product G=N×Q with N=C₆₈ and Q=C₄

		d	ρ	Label	ID
C₄×C₆₈		272		C4xC68	272,20

Semidirect products G=N:Q with N=C₆₈ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆₈⋊₁C₄ = C₆₈⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₆₈	68	4	C68:1C4	272,32
C₆₈⋊₂C₄ = C₄×C₁₇⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₆₈	68	4	C68:2C4	272,31
C₆₈⋊₃C₄ = C₆₈⋊₃C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₆₈	272		C68:3C4	272,13
C₆₈⋊₄C₄ = C₄×Dic₁₇	φ: C₄/C₂ → C₂ ⊆ Aut C₆₈	272		C68:4C4	272,11
C₆₈⋊₅C₄ = C₄⋊C₄×C₁₇	φ: C₄/C₂ → C₂ ⊆ Aut C₆₈	272		C68:5C4	272,22

Non-split extensions G=N.Q with N=C₆₈ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆₈.₁C₄ = D₃₄.₄C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₆₈	136	4	C68.1C4	272,30
C₆₈.₂C₄ = C₁₇⋊₃C₁₆	φ: C₄/C₁ → C₄ ⊆ Aut C₆₈	272	4	C68.2C4	272,3
C₆₈.₃C₄ = C₆₈.C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₆₈	136	4	C68.3C4	272,29
C₆₈.₄C₄ = C₆₈.₄C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₆₈	136	2	C68.4C4	272,10
C₆₈.₅C₄ = C₁₇⋊₄C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₆₈	272	2	C68.5C4	272,1
C₆₈.₆C₄ = C₂×C₁₇⋊₃C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₆₈	272		C68.6C4	272,9
C₆₈.₇C₄ = M₄(2)×C₁₇	φ: C₄/C₂ → C₂ ⊆ Aut C₆₈	136	2	C68.7C4	272,24

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