Generators and Representations for G = L₂(19)

Standard generators

• Standard generators of L₂(19) are a and b where a has order 2, b has order 3 and ab has order 19. (Source: ATLAS)
• Standard generators of the double cover 2.L₂(19) = SL₂(19) are preimages A and B where B has order 3 and AB has order 19. (Source: ATLAS)

BBOX programs

• Finder for L₂(19)
• Checker for L₂(19)
• CCL rep tester for L₂(19)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L2(19)	9	o	18(e)	χ2+χ3	Z			81%	3	2.0	perm rep on 171 pts
L2(19)	18	+	18(a)	χ4	C			76%		4.2	perm rep on 285 pts
			18(b)	χ5	C			76%		4.2	perm rep on 285 pts
			18(c)	χ6	C			75%		3.0	perm rep on 57 pts
			18(d)	χ7	C			75%		3.0	perm rep on 57 pts
			36(a)	χ4+χ5	Z			77%	26	6.3	perm rep on 285 pts
L2(19)	19	+	19	χ8	Z			89%	1	2.1	perm rep on 20 pts
L2(19)	20	+	20(a)	χ9	Z			72%	3	2.3	perm rep on 57 pts
2.L2(19)	10	o	No representations available
2.L2(19)	18	-	No representations available
2.L2(19)	20	-	No representations available

Last generated on Sat Sep 24 18:52:57 2005