[GAP Forum] How to recognize the conjugacy class of groups through their character table

[azhvan sanna]

Dear GAP Forum,

I asked a question while ago about calculating the value of characters on group elements, and we ended up ( upon now) with this answer that it's not possible to compute through "g^Xi" the value of any group element "g" under any character "Xi", as character table is just based on conjugacy class, and also those conjugacy classes has no label and are not based on specific representation of group from a generator set. 
As I deeply need to know how can i proceed my calculations ( which is about sporadic simple groups) I want to know any idea you guys can offer me. I need to calculate some things like this: suppose I have a generator set X for group G ( among sporadic simple group esp. some of big ones) after that for each Y in Irr(G) and for each t running from 1 to degree Y. I want to calculate sum of Y(x_1.x_2. .. x_t) over all x_i's from X. 

thanks so much

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