Extensions 1→N→G→Q→1 with N=C₅₄ and Q=C₂²

Direct product G=NxQ with N=C₅₄ and Q=C₂²

		d	ρ	Label	ID
C₂²xC₅₄		216		C2^2xC54	216,24

Semidirect products G=N:Q with N=C₅₄ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₄:C₂² = C₂²xD₂₇	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₄	108		C54:C2^2	216,23

Non-split extensions G=N.Q with N=C₅₄ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₄.₁C₂² = Dic₅₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₄	216	2-	C54.1C2^2	216,4
C₅₄.₂C₂² = C₄xD₂₇	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₄	108	2	C54.2C2^2	216,5
C₅₄.₃C₂² = D₁₀₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₄	108	2+	C54.3C2^2	216,6
C₅₄.₄C₂² = C₂xDic₂₇	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₄	216		C54.4C2^2	216,7
C₅₄.₅C₂² = C₂₇:D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₄	108	2	C54.5C2^2	216,8
C₅₄.₆C₂² = D₄xC₂₇	central extension (φ=1)	108	2	C54.6C2^2	216,10
C₅₄.₇C₂² = Q₈xC₂₇	central extension (φ=1)	216	2	C54.7C2^2	216,11

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