Clifford-Fischer theory applied to a group of the form 2_1+6:((31+2:8):2)
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In our paper [A. B. M. Basheer and J. Moori, On a group of the form 210:(U5(2):2)] we calculated the inertia factors, Fischer matrices and the ordinary character table of the split extension 210:(U5(2):2) by means of Clifford-Fischer Theory. The second inertia factor group of 210:(U5(2):2) is a group of the form 21+6−:((31+2:8):2). The purpose of this paper is the determination of the conjugacy classes of G¯¯¯¯ using the coset analysis method, the determination of the inertia factors, the computations of the Fischer matrices and the ordinary character table of the split extension G¯¯¯¯=21+6−:((31+2:8):2) by means of Clifford-Fischer Theory. Through various theoretical and computational aspects we were able to determine the structures of the inertia factor groups. These are the groups H1=H2=(31+2:8):2, H3=QD16 and H4=D12. The Fischer matrices Fi of G¯¯¯¯, which are complex valued matrices, are all listed in this paper and their sizes range between 2 and 5. The full character table of G¯¯¯¯, which is 41×41 complex valued matrix, is available in the PhD thesis of the first author, which could be accessed online.