Algebr Represent Theor (2014) 17:305–320 DOI 10.1007/s10468-012-9400-0 Characterizing Finite Quasisimple Groups by Their Complex Group Algebras Hung Ngoc Nguyen · Hung P. Tong-Viet Received: 25 June 2012 / Accepted: 12 December 2012 / Published online: 9 January 2013 © Springer Science+Business Media Dordrecht 2013 Abstract A finite group L is said to be quasisimple if L is perfect and L/ Z ( L) is nonabelian simple, in which case we also say that L is a cover of L/Z( L). It has been proved recently (Nguyen, Israel J Math, 2013) that a quasisimple classical group L is uniquely determined up to isomorphism by the structure of CL, the complex group algebra of L, when L/Z( L) is not isomorphic to PSL 3 (4) or PSU 4 (3). In this paper, we establish the similar result for these two open cases and also for covers with nontrivial center of simple groups of exceptional Lie type and sporadic groups. Together with the main results of Tong-Viet (Monatsh Math 166(3–4):559–577, 2012, Algebr Represent Theor 15:379–389, 2012), we obtain that every quasisimple group except covers of the alternating groups is uniquely determined up to isomorphism by the structure of its complex group algebra. Keywords Complex group algebras · Quasisimple groups · Exceptional groups · Groups of Lie type · Sporadic groups Mathematics Subject Classifications (2010) Primary 20C33 · 20C15 Presented by: Alain Verschoren. The second author is supported by a Startup Research Fund from the College of Agriculture, Engineering and Science, the University of KwaZulu-Natal. H. N. Nguyen Department of Mathematics, The University of Akron, Akron, OH 44325, USA e-mail: hungnguyen@uakron.edu H. P. Tong-Viet (B ) School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg 3209, South Africa e-mail: Tongviet@ukzn.ac.za