Abstract

PRINS, Abraham Love. On the Fischer matrices of a group of shape 2 ¹⁺²ⁿ ₊:G. Rev.colomb.mat. [online]. 2022, vol.56, n.2, pp.189-211.  Epub Feb 06, 2024. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v56n2.108379.

In this paper, the Fischer matrices of the maximal subgroup G = 21+8 +: (U 4(2):2) of U 6(2):2 will be derived from the Fischer matrices of the quotient group Q = G/Z(21+8 +) ( 28: (U 4(2):2), where Z(21+8 +) denotes the center of the extra-special 2-group 21+8 +. Using this approach, the Fischer matrices and associated ordinary character table of G are computed in an elegantly simple manner. This approach can be used to compute the ordinary character table of any split extension group of the form 2 1+2n +: G, n ∈ N, provided the ordinary irreducible characters of 2 1+2n + extend to ordinary irreducible characters of its inertia subgroups in 2 1+2n +:G and also that the Fischer matrices M(g i ) of the quotient group 2 1+2n +: G/Z(2 1+2n +) ( 2 2n: G are known for each class representative g i in G.

Keywords : split extension; extra-special p-group; irreducible projective characters; Schur multiplier; inertia factor groups; Fischer matrices.

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