Sporadic Mathieu group M11
Order = 7 920 = 24.32.5.11.
Mult = 1.
Out = 1.
Robert Wilson's ATLAS page for the Mathieu group M11 is available here.
M11: Length 65, 2-generator, 5-relator.
< x, y | x2 = y4 = (xy)11 = (xy2)6 = xyxyxy-1xyxy2xy-1xyxy-1xy-1 = 1 >
Remark: x and y are (R.A.Wilson's) standard generators for M11.
Reciprocity: (x, y) and (x, y-1) are not conjugate in Aut(M11) = M11.
M11: Length 64, 2-generator, 5-relator.
< x, y | x2 = y5 = (xy)8 = (xyxy-1xy2)3 = xyxyxy-1xy-1xy-2xy-2xy2xy2 = 1 >
Remark: The relations (xy2)11 = [x, y]5 = 1 hold.
Reciprocity: (x, y), (x, y2), (x, y-2) and (x, y-1) are not conjugate in Aut(M11) = M11.
M11: Length 88, 2-generator, 6-relator.
< x, y | x2 = y5 = (xy)8 = [x, y]5 = (xyxy-1xy2)3 = (xyxy-2xy2)3 = 1 >
Remark: This presentation is on the same generators as the previous one.
Reciprocity: (x, y), (x, y2), (x, y-2) and (x, y-1) are not conjugate in Aut(M11) = M11.
M11 × D10: Length 43, 2-generator, 4-relator.
< x, y | x2 = y5 = (xy)8 = xyxyxy-1xy-1xy-2xy-2xy2xy2 = 1 >
Remark: The relations (xy2)22 = [x, y]5 = 1 hold.
Reciprocity: (x, y), (x, y2), (x, y-2) and (x, y-1) are not conjugate in Aut(G).
Last updated 30th August, 1997
John N. Bray