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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊C₅₄ = C₂²×C₉.A₄	φ: C₅₄/C₁₈ → C₃ ⊆ Aut C₂³	108		C2^3:C54	432,225
C₂³⋊₂C₅₄ = D₄×C₅₄	φ: C₅₄/C₂₇ → C₂ ⊆ Aut C₂³	216		C2^3:2C54	432,54

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.C₅₄ = C₄×C₉.A₄	φ: C₅₄/C₁₈ → C₃ ⊆ Aut C₂³	108	3	C2^3.C54	432,40
C₂³.₂C₅₄ = C₂²⋊C₄×C₂₇	φ: C₅₄/C₂₇ → C₂ ⊆ Aut C₂³	216		C2^3.2C54	432,21

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