Generators and Representations for G = L₃(13)

Standard generators

• Standard generators of L₃(13) are a and b where a has order 2, b has order 3 and ab has order 61. (Source: thesis)
• Standard generators of the triple cover 3.L₃(13) = SL₃(13) are preimages A and B where A has order 2 and AB has order 61. (Source: thesis)

BBOX programs

• Finder for L₃(13)
• Checker for L₃(13)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L3(13)	182	+	182	χ2	Z			99%	1	136.4	perm rep on 183 pts
L3(13)	183	+	183(a)	χ3	Z			99%	1	137.7	perm rep on 366 pts
L3(13)	183	o	183(b)	χ4	Z(i)			99%		137.8	induced from Borel subgroup
			183(c)	χ5	Z(i)			99%		137.8	induced from Borel subgroup
			366	χ4+χ5	Z			99%	1	549.7	induced from Borel subgroup (blown up)
3.L3(13)	183	o	No representations available

Notes

There appear to be two types of indicator 0 representations of dimension 183 for 3.L3(13). They will need to be distinguished somehow.

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