Character tables of the association schemes of finite orthogonal groups acting on the nonisotropic points

RATIONAL CHARACTER TABLE OF SOME FINITE GROUPS

The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational character tables are also considered into account.The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational charact...

On the non-split extension group $2^{6}{^{cdot}}Sp(6,2)$

In this paper we first construct the non-split extension $overline{G}= 2^{6} {^{cdot}}Sp(6,2)$ as a permutation group acting on 128 points. We then determine the conjugacy classes using the coset analysis technique, inertia factor groups and Fischer matrices, which are required for the computations of the character table of $overline{G}$ by means of Clifford-Fischer Theory. There are two inerti...

On the Mark and Markaracter Tables of Finite Groups

Let G be a finite group and C(G) be the family of representative conjugacy classes of‎ ‎subgroups of G‎. ‎The matrix whose H,K-entry is the number of ‎fixed points of the set G/K under the action of H is called the‎ ‎table of marks of G where H,K run through all elements in‎ C(G)‎. Shinsaku Fujita for the first time introduced the term “markaracter” to discuss marks for permutation representati...

Association schemes of a‰ne type over finite rings

Kwok [10] studied the association schemes obtained by the action of the semidirect products of the orthogonal groups over the finite fields and the underlying vector spaces. They are called the assiciation schemes of a‰ne type. In this paper, we define the association schemes of a‰ne type over the finite ring Zq 1⁄4 Z=qZ where q is a prime power in the same manner, and calculate their character...

On Some Relationships Among the Association Schemes of Finite Orthogonal Groups Acting on Hyperplanes