Sporadic Janko group J₃

Order = 50 232 960 = 2⁷.3⁵.5.17.19.
Mult = 3.
Out = 2.

Robert Wilson's ATLAS page for the Janko group J₃ is available here.

J₃: Length ??, ?-generator, ?-relator.

J₃:2: Length 134, 4-generator, 11-relator.

< a, b, c, d | a¹⁷ = b⁸ = a^ba^-2 = c² = b^cb³ = (abc)⁴ = (ac)¹⁷ = d² = [d, a] = [d, b] = (a³b^-3cd)⁵ = 1 >

Remark: This is the progenitor 2^*120:(L₂(16):4) factored by a single relation (namely (a³b^-3cd)⁵ = 1). We have that N = < a, b, c > = L₂(16):4 of index 6156 is the control subgroup.

Last updated 16^th July, 1997

John N. Bray

Sporadic Janko group J3

J3: Length ??, ?-generator, ?-relator.

J3:2: Length 134, 4-generator, 11-relator.

Sporadic Janko group J₃

J₃: Length ??, ?-generator, ?-relator.

J₃:2: Length 134, 4-generator, 11-relator.