ON AN INERTIA FACTOR GROUP OF 2\(^8\):\(O_8^+\)(2) - Moori, Jamshid; Seretlo, Thekiso (Italian Journal of Pure and Applied Mathematics, 2014)
ON AN INERTIA FACTOR GROUP OF 2\(^8\):\(O_n ^+\)(2) The group \(G\) = 26:A8 is an inertia factor group of 2\(^8\):\(O_8^+\)(2). As an inertia factor group, our group \(G\) plays an essential role in the construction of the character table of 2\(^8\):\(O_n ^+\)(2). In this paper we look at two ways of constructing \(G\). In the first method, we use combinatorics and the natural action of A8 on W \(\) 26. In the second method, we use a computational method to construct \(G\) = N:A8 inside \(O_8^+\)(2). We show that A8 acts irreducibly on both W and N and we prove that the two groups are indeed isomorphic.