Generators and Representations for G = L₃(3)

Standard generators

• Standard generators of L₃(3) are a and b where a has order 2, b is in class 3B and ab is in class 13A/B. The last condition is equivalent to: ab has order 13 and ababb has order 4. Wlog define 13A to be the class containing ab, and then 8B is the class containing abababb. (Source: ATLAS)

BBOX programs

• Finder for L₃(3)
• Checker for L₃(3)
• CCL rep tester for L₃(3)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L3(3)	12	+	12	χ2	Z			87%	1	1.1	perm rep on 13 pts
L3(3)	13	+	13	χ3	Z			73%	2	1.2	perm rep on 144 pts
L3(3)	16	o	64	χ4+χ5+χ6+χ7	Z			86%	7	17.7	perm rep on 144 pts
L3(3)	26	+	26(a)	χ8	Z			95%	1	3.2	perm rep on 39(a) pts
L3(3)	26	o	26(b)	χ9	C			95%		3.3	induced 2-dimensional rep of 3^2:2S4, faithful on 2S4 (Nazarov partition [4])
			26(c)	χ10	C			95%		3.3	complex conjugate of χ9
			52	χ9+χ10	Z			92%	5	11.8	perm rep on 234b pts
L3(3)	27	+	27	χ11	Z			70%	6	3.6	perm rep on 144 pts
L3(3)	39	+	39	χ12	Z			72%	12	7.2	perm rep on 144 pts

Notes

Element xyxyxy² is in class 8A.

Last generated on Sat Sep 24 18:53:00 2005