Generators and Representations for G = J₁

Standard generators

• Standard generators of the Janko group J₁ are a and b where a has order 2, b has order 3, ab has order 7 and ababb has order 19. (Source: ATLAS)

BBOX programs

• Finder for J₁
• Checker for J₁
• CCL rep tester for J₁

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
J1	56	+	112	χ2+χ3	Z			82%	19	54.4	perm rep on 296 pts
J1	76	+	76(a)	χ4	Z			77%	15	25.6	perm rep on 266 pts
			76(b)	χ5	Z			58%	29	26.9	perm rep on 1596 pts
J1	77	+	77(a)	χ6	Z			93%	16	25.2	perm rep on 266 pts
			154(a)	χ7+χ8	Z			72%	70	107.3	perm rep on 1045 pts
J1	120	+	360	χ9+χ10+χ11	Z			77%	2582	640.3	perm rep on 1045 pts
J1	133	+	133(a)	χ12	Z			50%	783	100.5	perm rep on 1045 pts
			266	χ13+χ14	Z			65%	4118	397.1	perm rep on 1596 pts
J1	209	+	209	χ15	Z			79%	276	198.3	perm rep on 1045 pts

Last generated on Sat Sep 24 18:52:39 2005