48.32 ClassStructureCharTable

ClassStructureCharTable( tbl, classes )

returns the so--called class structure of the classes in the list classes, for the character table tbl of the group G. The length of classes must be at least 2.

    gap> t:= CharTable( "M12" );;
    gap> ClassStructureCharTable( t, [2,6,9,13] );
    916185600
    gap> ClassStructureCharTable( t, [2,9,13] ); # equals the group order
    95040

Let C_1, dots, C_n denote the conjugacy classes of G that are indexed by classes. The class structure n(C_1, C_2, ldots, C_n) equals the number of tuples (g_1, g_2, ldots, g_n) of elements g_i in C_i with g_1 g_2 cdots g_n = 1. Note the difference to the definition of the class multiplication coefficients in ClassMultCoeffCharTable ClassMultCoeffCharTable.

n(C_1, C_2, ldots, C_n) is computed using the formula [ n(C_1, C_2, ldots, C_n) = frac|C_1||C_2|cdots|C_n||G| sum_chi in mboxfootnotesize Irr(G) fracchi(g_1)chi(g_2)cdotschi(g_n)chi(1)^n-2 . ]

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