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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]

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]

The symplectic groupSp(6, 2) has a 14−dimensional absolutely irreducible module over. Hence a split extension group of the formḠ= 214:Sp(6,2) does exist. In this paper we first determine the conjugacy classes ofḠusing the coset analysis technique. The structures of inertia factor groups were determined. The inertia factor groups areSp(6, 2), (21+4× 22):(S3×S3),S3×S6,PSL(2, 8), (((22×Q8):3):2):2,S3×A5,and 2×S4×S3.We then determine the Fischer matrices and apply the Clifford-Fischer theory to compute the ordinary character table of.The Fischer matrices ofare all integer valued, with size ranging from 4 to 16. The full character table ofis a 186×186 complex valued matrix. [ABSTRACT FROM PUBLISHER]