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Dear Gap Forum, dear Edgar,

I am interested in finding the irreducible representations of GL(2,n) -

the group of 2-by-2 invertible matrices with integer entries modulo n.

Here, n is not necessarily a power of a prime number. How can I use Gap

to find these irreducible representations?

As far as I know, up to now there is no built-in automatic mechanism

in GAP to compute the irreducible representations of an arbitrary

finite group. (The situation is different for special classes of

groups, which unfortunately the GL_2(Z/nZ)'s do not belong to.) But

there are so-called `MeatAxe' techniques available to find irreducible

representations rather comfortably by hand. There is a GAP share

package which works over finite fields, and I have (private, still)

programs which (are supposed to) do the job over the rationals and

finite extension fields thereof.

These programs might be useful for the examples you have, Edgar; if

you are interested, please do not hesitate to contact me. Possibly I

can then give you more specific advice.

Best, J"urgen M"uller.

Miles-Receive-Header: reply

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