ATLAS: Janko group J3

Order = 50232960.
Mult = 3.
Out = 2.

Standard generators

Standard generators of the Janko group J3 are a and b where a has order 2, b is in class 3A, ab has order 19, and ababb has order 9.
Standard generators of the triple cover 3J3 are pre-images A and B where A has order 2, and B is in class +3A.
Standard generators of the automorphism group J3:2 are c and d where c is in class 2B, d is in class 3A, cd has order 24, and cdcdd has order 9.
Standard generators of 3J3:2 are preimages C and D, where D is in class +3A.
A pair of generators conjugate to a, b can be obtained as
a' = (cd)^{12}, b' = (cdcdd)^{-1}dcdcdd.

Black box algorithms

To find standard generators for J3: To find standard generators for J3.2:

Representations

NB: As usual, the ordering of the representations [and their labellings] is NOT guaranteed to remain constant unless explicitly indicated to the contrary.

The representations of J3 available are

The representations of 3J3 available are The representations of J3:2 available are The representations of 3J3:2 available are

Maximal subgroups

The maximal subgroups of J3 are as follows. Words are given by Suleiman and Wilson in Experimental Math. 4 (1995), 11-18. The maximal subgroups of J3:2 are as follows. Words are given by Suleiman and Wilson in Experimental Math. 4 (1995), 11-18.

Conjugacy classes

A set of generators for the maximal cyclic subgroups can be obtained by running this program on the standard generators. All conjugacy classes can therefore be obtained as suitable powers of these elements.
- Return to main ATLAS page. - Last updated 29.10.99

- R.A.Wilson@bham.ac.uk
- richard@ukonline.co.uk