Linear group L2(13)
Order = 1 092 = 22.3.7.13.
Mult = 2.
Out = 2.
Robert Wilson's ATLAS page for L2(13) is available here.
L2(13): Length 43, 2-generator, 4-relator.
< x, y | x2 = y3 = (xy)7 = [x, y]6 = 1 >
Remark: This is the Coxeter group (2, 3, 7; 6).
L2(13): Length 47, 2-generator, 4-relator.
< x, y | x2 = y3 = (xy)7 = [x, y]7 = 1 >
Remark: This is the Coxeter group (2, 3, 7; 7).
L2(13): Length 49, 2-generator, 4-relator.
< x, y | x2 = y3 = (xy)7 = (xyxyxy-1xyxy-1)3 = 1 >
Remark: In this group [x, y] has order 13.
L2(13): Length 67, 2-generator, 4-relator.
< x, y | x2 = y3 = (xy)13 = ((xy)5xy-1(xy)2xy-1)2 = 1 >
Remark: JGS-presentation ((2, 3, p)-generated version). x and y are R.A.Wilson's standard generators for L2(13).
L2(13): Length 69, 3-generator, 7-relator.
< a, b, c | a2 = b2 = c2 = (ab)3 = (ac)2 = (bc)7 = (abc)13 = 1 >
Remark: This is the Coxeter group G3,7,13.
PGL2(13): Length 66, 3-generator, 7-relator.
< a, b, c | a2 = b2 = c2 = (ab)3 = (ac)2 = (bc)7 = (abc)12 = 1 >
Remark: This is the Coxeter group G3,7,12.
PGL2(13): Length 72, 3-generator, 7-relator.
< a, b, c | a2 = b2 = c2 = (ab)3 = (ac)2 = (bc)7 = (abc)14 = 1 >
Remark: This is the Coxeter group G3,7,14.
Last updated 16th July, 1997
John N. Bray