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Shreyasi Acharya, Jaroslav Adam, Dagmar Adamová, Jonatan Adolfsson, Madan Mohan Aggarwal, Gianluca Aglieri Rinella, Michelangelo Agnello, Neelima Agrawal, Zubayer Ahammed, Nazeer Ahmad, Sang Un Ahn, Salvatore Aiola, Alexander Akindinov, Mohammad Al-Turany, Sk Noor Alam, José Luis Bazo Alba, Danilo Silva de Albuquerque, Dmitry Aleksandrov, Bruno Alessandro, Jose Ruben Alfaro Molina, Andrea Alici, Anton Alkin, Johan Alme, Torsten Alt, Lucas Altenkämper, Igor Altsybeev, Caio Alves Garcia Prado, Cristian Andrei, Dimitra Andreou, Harry Arthur Andrews, Anton Andronic, Venelin Anguelov, Christopher Daniel Anson, Tome Antičić, Federico Antinori, Pietro Antonioli, Rafay Anwar, Laurent Bernard Aphecetche, Harald Appelshäuser, Silvia Arcelli, Roberta Arnaldi, Oliver Werner Arnold, Ionut Cristian Arsene, Mesut Arslandok, Benjamin Audurier, Andre Augustinus, Ralf Peter Averbeck, Mohd Danish Azmi, Angela Badalà, Yong Wook Baek, Stefano Bagnasco, Raphaëlle Bailhache, Renu Bala, Alberto Baldisseri, Markus Ball, Rama Chandra Baral, Anastasia Maria Barbano, Roberto Barbera, Francesco Barile, Luca Barioglio, Gergely Gábor Barnaföldi, Lee Stuart Barnby, Valerie Ramillien Barret, Paolo Bartalini, Klaus Barth, Esther Bartsch, Maurizio Basile, Nicole Bastid, Sumit Basu, Guillaume Batigne, Boris Batyunya, Paul Christoph Bätzing, Ian Gardner Bearden, Hans Beck, Cristina Bedda, Nirbhay Kumar Behera, Iouri Belikov, Francesca Bellini, Hector Bello Martinez, Rene Bellwied, Lucina Gabriela Espinoza Beltran, Vladimir Belyaev, Gyula Bencédi, Stefania Beolè, Alexandru Bercuci, Yaroslav Berdnikov, Dániel Berényi, Redmer Alexander Bertens, Dario Berzano, Latchezar Betev, Anju Bhasin, Inayat Rasool Bhat, Ashok Kumar Bhati, Buddhadeb Bhattacharjee, Jihyun Bhom, Antonio Bianchi, Livio Bianchi, Nicola Bianchi, Chiara Bianchin, Jaroslav Bielčík, Jana Bielčíková, Ante Bilandzic, Gabor Biro, Rathijit Biswas, Saikat Biswas, Justin Thomas Blair, Dmitry S. 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• The correlations between event-by-event fluctuations of anisotropic flow harmonic amplitudes have been measured in Pb-Pb collisions at sNN−−−√ = 2.76 TeV with the ALICE detector at the LHC. The results are reported in terms of multiparticle correlation observables dubbed Symmetric Cumulants. These observables are robust against biases originating from nonflow effects. The centrality dependence of correlations between the higher order harmonics (the quadrangular v4 and pentagonal v5 flow) and the lower order harmonics (the elliptic v2 and triangular v3 flow) is presented. The transverse momentum dependence of correlations between v3 and v2 and between v4 and v2 is also reported. The results are compared to calculations from viscous hydrodynamics and A Multi-Phase Transport ({AMPT}) model calculations. The comparisons to viscous hydrodynamic models demonstrate that the different order harmonic correlations respond differently to the initial conditions and the temperature dependence of the ratio of shear viscosity to entropy density (η/s). A small average value of η/s is favored independent of the specific choice of initial conditions in the models. The calculations with the AMPT initial conditions yield results closest to the measurements. Correlations between the magnitudes of v2, v3 and v4 show moderate pT dependence in mid-central collisions. Together with existing measurements of individual flow harmonics, the presented results provide further constraints on the initial conditions and the transport properties of the system produced in heavy-ion collisions.