Clifford-Fischer theory applied to a group of the form 2_1+6:((31+2:8):2)

Abstract

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.