Nagoya Mathematical Journal

The Schur multipliers of the Mathieu groups

N. Burgoyne and P. Fong

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Nagoya Math. J., Volume 27, Part 2 (1966), 733-745.

First available in Project Euclid: 14 June 2005

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Primary: 20.25


Burgoyne, N.; Fong, P. The Schur multipliers of the Mathieu groups. Nagoya Math. J. 27 (1966), no. 2, 733--745.

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  • [8] R. G. Stanton, The Mathieu groups, Can. Jour. Math. Vol 3 (1951), pp. 164-174. Tables In Tables 1, 2, 3 the first column describes the conjugacy class by giving its cycle structure in the natural permutation representation of that group. The second column is the order h of the centralizer subgroup of an element in that class. A character written with a bar above it denotes a pair of complex- conjugate characters.Recall that the orders of the Mathieu groups are hn, A 12.Aii, fe, fes 23.fc, /z24 24.fe. In Table 4 we give the character (see 2 of part II) for the Mn subgroup in Mi2.We only list those classes on which the character is non-zero.In Table 5 we list the values of for f23 in Mu only on those classes for which they are needed in 3 of part II. In Table 6 we only give a single value for the projective character. The other values on each splitting class are multiples of the given value by -g-( - 1U 3).