Generators and Representations for G = L₂(13)

Standard generators

• Standard generators of L2(13) are a and b where a has order 2, b has order 3 and ab has order 13. (Source: ATLAS)
• Standard generators of the double cover 2.L2(13) = SL2(13) are pre-images A and B where B has order 3 and AB has order 13. (Source: ATLAS)

BBOX programs

• Finder for L₂(13)
• Checker for L₂(13)
• CCL rep tester for L₂(13)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L2(13)	7	+	7(a)	χ2	C			73%		1.4	χ3 *2
			7(b)	χ3	C			73%		1.5	perm rep on 28 pts
			14(c)	χ2+χ3	Z			92%	1	1.4	perm rep on 28 pts
L2(13)	12	+	12(a)	χ4	C			81%		1.7	perm rep on 78 pts, reseeded with b+ab+bb(ab)^11-1
			12(b)	χ5	C			81%		1.6	perm rep on 78 pts, [4] *4
			12(c)	χ6	C			81%		1.6	perm rep on 78 pts, [5] *4
			36	χ4+χ5+χ6	Z			70%	7	6.4	perm rep on 78 pts
L2(13)	13	+	13	χ7	Z			88%	1	1.3	perm rep on 14 pts
L2(13)	14	+	14(a)	χ8	Z			85%	1	1.4	induce from Borel, reseed
			14(b)	χ9	Z			81%	1	1.4	induce from Borel, reseed
2.L2(13)	6	-	No representations available
2.L2(13)	12	-	No representations available
2.L2(13)	14	-	No representations available

Notes

Identifying classes: ababb is class 7A, ab is class 13A.

Last generated on Sat Sep 24 18:52:56 2005