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...

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.

A method for character-string recognition is presented. The proposed method jointly evaluates features obtained from individual characters and inter-character spaces. Combining these features resolves ambiguity in segmentation and classification of low-quality character-string images. To evaluate the inter-character features, an intercharacter orthogonal subspace is constructed for each permuta...

There are many combinatorial expressions for evaluating characters of the Hecke algebra of type A. However, with rare exceptions, they give simple results only for permutations that have minimal length in their conjugacy class. For other permutations, a recursive formula has to be applied. Consequently, quantum immanants are complicated objects when expressed in the standard basis of the quantu...

A representation of a group is a realization of its elements in terms of matrices that takes the group operation into matrix multiplication. The groups of permutations (symmetric groups) were among the first families of groups for which the representations were classified in the work of Frobenius, Schur and Young around 1900. It was found that the irreducible representations of the nth permutat...

This note shows a few examples of GAP computations concerning multiplicity-free permutation characters, with an emphasis on the classification of the faithful multiplicity-free permutation characters of the sporadic simple groups and their automorphism groups given in [BL96]. For examples on GAP computations with permutation characters in general, see the note [Bre]. For further questions about...

Archie (1989), Faith (1990), and Faith and Cranston (1991) devised a test for phylogenetic structure in character data sets, which Faith and Cranston called the permutation tail probability (PTP) test. Faith (1991) introduced a reŽnement intended to test the strength of support for monophyly of individual clades, which he called the topologydependent permutation tail probability (T-PTP) test. F...