Sporadic Janko group J1
Order = 175 560 = 23.3.5.7.11.19.
Mult = 1.
Out = 1.
Robert Wilson's ATLAS page for the Janko group J1 is available here.
J1: Length 44, 3-generator, 7-relator.
< x, y, t | x5 = y3 = (xy)2 = t2 = [y, t] = [y, x2tx-2] = (xt)7 = 1 >
Remark: RTC-presentation. This is the progenitor 2*5:A5 factored out by the relation [(0, 1, 2, 3, 4)t0]7 = 1.
J1: Length 123, 2-generator, 5-relator.
< x, y | x2 = y3 = (xy)7 = [x, y]11 = (xyxyxy-1xyxy-1xy-1)5 = 1 >
Remark: Closely related to the CR-presentation 15.3.
Last updated 16th July, 1997
John N. Bray