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Dear GAP Forum,

Vahid Dabbaghian asked:

How can I get the character value of an element of group G,

without checking that this element is in which conjugacy class

of G.

This depends a bit ob the representation G is given in, as well as the

representation that affords the character:

If G is a matrix group, and the character is given by the natural matrix

representation of G, you can use TraceMat.

If the character is given by the natural permutation representation, you can

check the number of fixed points:

Number(MovedPoints(G),x->x^g=x);

Otherwise you'll somehow have to connect the group and the representation.

If you can define the representation as a homomorphism, you can use the trace of

the image of an element (though you should be aware that for very large groups

the calculation of homomorphism images might be tedious).

Otherwise I don't see a way how you could (even in theory) get the character

value without (at least implicitly) identifying the class of the element.

If this does not answer your question please give us a bit more detail about

what group and what character you are looking at.

Best wishes,

Alexander Hulpke

-- Colorado State University, Department of Mathematics,

Weber Building, Fort Collins, CO 80523, USA

email: hulpke@math.colostate.edu

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