Generators and Representations for G = L₄(3)

Standard generators

• Standard generators of L₄(3) are a and b where a is in class 2A, b is in class 4B, ab has order 13 and abb has order 8. The last condition is equivalent to ababb has order 13. These conditions ensure that ab is in class 13A/B. (Source: ATLAS)
• Standard generators of the double cover 2.L₄(3) are preimages A and B where AB has order 13 and ABABB has order 13. (Source: ATLAS)

BBOX programs

• Checker for L₄(3)
• CCL rep tester for L₄(3)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L4(3)	26	+	26(a)	χ2	Z			88%	2	3.3	perm rep on 117a pts
			26(b)	χ3	Z			88%	3	3.3	perm rep on 117b pts
L4(3)	39	+	39	χ4	Z			94%	1	6.9	perm rep on 40 pts (either of them)
L4(3)	52	+	52	χ5	Z			87%	11	11.9	perm rep on 234a pts
L4(3)	65	+	65(a)	χ6	Z			90%	4	18.1	perm rep on 234a pts
			65(b)	χ7	Z			91%	3	18.1	perm rep on 234b pts
L4(3)	90	+	90	χ8	Z			95%	2	34.0	perm rep on 130 pts
L4(3)	234	+	234(a)	χ9	Z			97%	4	226.6	perm rep on 340 pts
			234(b)	χ10	Z			95%	7	227.4	2_1 automorph of χ9
2.L4(3)	40	+	No representations available
2.L4(3)	208	o	No representations available

Notes

xy³xy²xyxyxyxy is in class 9B. xy²xy³xy is in class 12A.

Last generated on Sat Sep 24 18:53:03 2005