The group GL(2,4) and subgroups

From: Van Jacques (calccurve-test23_at_yahoo.com)
Date: 08/03/04 

Date: 3 Aug 2004 06:41:57 -0700

I wanted to look at the group GL(2,4), where the field
is F_4 = (0, 1, x, x^2 = x + 1), since the only irred deg 2
poly over Z_2 is x^2 + x + 1. (Also SL(2,4), PGL(2,4) PSL(2,4).)

I have looked at GL(2,2) = S_3, and GL(2,3) and SL(2,3), PSL(2,3),
PGL(2,3). I forget if one gives S_4 or not, but I know that
(at least) one gives A_4.

I have never seen anyone do anything with F_4 though.
I have seen a prob. referring to GL(2,5) or one of its subgroups
in Lang, I think, though I never did it.

I wonder how many elements there are in GL(2,4)?

I recall the formula n = p(p - 1)(p^2 - 1) for p prime,
and it would give 180 if p = 4, but I don't think that
will work.

I suppose I should not take the easy out of posting
this here till I thought about it longer, but you
people always have such good ideas ;-)

Van

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