Extensions 1→N→G→Q→1 with N=C₅₄ and Q=C₂³

Direct product G=N×Q with N=C₅₄ and Q=C₂³

		d	ρ	Label	ID
C₂³×C₅₄		432		C2^3xC54	432,228

Semidirect products G=N:Q with N=C₅₄ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₄⋊C₂³ = C₂³×D₂₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₄	216		C54:C2^3	432,227

Non-split extensions G=N.Q with N=C₅₄ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₄.₁C₂³ = C₂×Dic₅₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₄	432		C54.1C2^3	432,43
C₅₄.₂C₂³ = C₂×C₄×D₂₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₄	216		C54.2C2^3	432,44
C₅₄.₃C₂³ = C₂×D₁₀₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₄	216		C54.3C2^3	432,45
C₅₄.₄C₂³ = D₁₀₈⋊₅C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₄	216	2	C54.4C2^3	432,46
C₅₄.₅C₂³ = D₄×D₂₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₄	108	4+	C54.5C2^3	432,47
C₅₄.₆C₂³ = D₄⋊₂D₂₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₄	216	4-	C54.6C2^3	432,48
C₅₄.₇C₂³ = Q₈×D₂₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₄	216	4-	C54.7C2^3	432,49
C₅₄.₈C₂³ = Q₈⋊₃D₂₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₄	216	4+	C54.8C2^3	432,50
C₅₄.₉C₂³ = C₂²×Dic₂₇	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₄	432		C54.9C2^3	432,51
C₅₄.₁₀C₂³ = C₂×C₂₇⋊D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₅₄	216		C54.10C2^3	432,52
C₅₄.₁₁C₂³ = D₄×C₅₄	central extension (φ=1)	216		C54.11C2^3	432,54
C₅₄.₁₂C₂³ = Q₈×C₅₄	central extension (φ=1)	432		C54.12C2^3	432,55
C₅₄.₁₃C₂³ = C₄○D₄×C₂₇	central extension (φ=1)	216	2	C54.13C2^3	432,56

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