Generators and Representations for G = J₃

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. (Source: ATLAS)
• Standard generators of the triple cover 3.J₃ are preimages A and B where A has order 2 and B is in class +3A. The condition that B is in class +3A is equivalent to the condition that ABABABB has order 17. (Source: ATLAS)
• 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. (Source: ATLAS)

BBOX programs

• Finder for J₃
• Finder for J₃.2
• Checker for J₃
• Checker for J₃.2
• CCL rep tester for J₃

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
J3	85	o	170	χ2+χ3	Z			62%	246	144.1	perm rep on 14688 pts
3.J3	18	o	No representations available
3.J3	153	o	No representations available
3.J3	171	o	No representations available

Last generated on Sat Sep 24 18:52:40 2005