Linear group L2(16)
Order = 4 080 = 24.3.5.17.
Mult = 1.
Out = 4.
Robert Wilson's ATLAS page for L2(16) is available here.
L2(16): Length 48, 2-generator, 5-relator.
< x, y | x3 = y5 = (x-1yxy)2 = (x-1y2xy2)2 = (xxy)5 = 1 >
L2(16): Length 40, 3-generator, 6-relator.
< a, b, c | a2 = b15 = c2 = b-4ab3aba = (ac)3 = (bc)2 = 1 >
L2(16): Length 97, 2-generator, 5-relator.
< x, y | x2 = y3 = (xy)15 = (xyxyxy-1xyxy-1)3 = (xyxyxyxyxyxy-1xy-1xy-1)2 = 1 >
Remark: x and y are R.A.Wilson's standard generators for L2(16).
L2(16): Length 101, 2-generator, 5-relator.
< x, y | x2 = y3 = (xy)17 = (xyxyxyxy-1xy-1)3 = (xyxyxy-1xyxyxy-1xyxy-1)2 = 1 >
L2(16): Length 71, 2-generator, 4-relator.
< x, y | x2 = y3 = (xy)17 = (xyxyxyxy-1xyxyxy-1xy-1)2 = 1 >
Remark: The coset enumeration may work better if we include the relation (xyxyxy-1xyxy-1xyxy-1)3 = 1.
L2(16) x 3: Length 28, 2-generator, 4-relator.
< x, y | x3 = y5 = (x-1yxy)2 = (x-1y2xy2)2 = 1 >
Last updated 16th July, 1997
John N. Bray