the group $2^6{{}^{cdot}} g_2(2)$ is a maximal subgroup of the rudvalis group $ru$ of index 188500 and has order 774144 = $2^{12}.3^3.7$. in this paper, we construct the character table of the group $2^6{{}^{cdot}} g_2(2)$ by using the technique of fischer-clifford matrices.

We characterize topological spaces which are coset of (separable) metrizable groups and complete (Polish) groups. Moreover, it is shown that for a $G$-space $X$ with $d$-open action there group $H$ weight cardin

In heterotic string theory compactified on T , the T-duality orbits of dyons of charge (Q,P ) are characterized by O(6, 22; R ) invariants Q, P 2 and Q · P together with a set of invariants of the discrete T-duality group O(6, 22; ZZ). We study the action of S-duality group on the discrete T-duality invariants and study its consequence for the dyon degeneracy formula. In particular we find that...

There are q+q right PGL2(Fq)−cosets in the group PGL2(Fq2). In this paper, we present a method of generating all the coset representatives, which runs in time Õ(q), thus achieves the optimal time complexity up to a constant factor. Our algorithm has applications in solving discrete logarithms and finding primitive elements in finite fields of small characteristic.