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Let G be a finite group and X be a conjugacy class of G. The rank of X in G, denoted by rank(G : X), is defined to be the minimum number of elements of X generating G. We investigate the ranks of the alternating group A11. We use the structure constants method to determine the ranks of all the non-trivial classes of the group A11. [ABSTRACT FROM AUTHOR]

A finite group G is called (l,m, n)-generated, if it is a quotient group of the triangle group T (l,m, n) = . In [24], Moori posed the question of finding all the (p, q, r) triples, where p, q and r are prime numbers, such that a non-abelian finite simple group G is a (p, q, r)-generated. In this paper we will establish all the (p, q, r)-generations of the Mathieu group M22. GAP [16] and the Atlas of finite group representations [30] are used in our computations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is the determination of the inertia factors, the computations of the Fischer matrices and the ordinary character table of the split extension G¯ = 37:Sp(6; 2) by means of Clifford-Fischer Theory. We firstly determine the conjugacy classes of G¯ using the coset analysis method. The determination of the inertia factor groups of this extension involved looking at some maximal subgroups of the maximal subgroups of Sp(6; 2): The Fischer matrices of G¯ are all listed in this paper and their sizes range between 2 and 10. The character table of G¯, which is a 118 × 118 C-valued matrix, is available in the PhD thesis of the first author, which could be accessed online. [ABSTRACT FROM AUTHOR]