Type A standard generators of W(F4) are involutions a, b, c and d such that ab, ac, ad, bc, bd and cd have orders 3, 2, 2, 4, 2 and 3 respectively. These generators satisfy the standard presentation of W(F4).
Type B standard generators of W(F4) are x and y where x is in class 2C (see below), y has order 6, xy has order 6 and xyy has order 4.
We may take x = bd and y = acd.
Conversely, we have a = y3, b = x(xy3)3, c = yxy3xy3x and d = (xy3)3.
< x, y | x2 = y6 = (xy)6 = (xy2)4 = (xyxyxy-2)2 = 1 >.
The centre is generated by [x, y]3.
Last updated 24th April 1998,