Generators and Representations for G = G₂(3)

Standard generators

• Standard generators of G₂(3) are a and b where a has order 2, b is in class 3C and ab has order 13. (Source: ATLAS)
• Standard generators of the triple cover 3.G₂(3) are preimages A and B where A has order 2 and AB has order 13. (Source: ATLAS)

BBOX programs

• Checker for G₂(3)
• CCL rep tester for G₂(3)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
G2(3)	14	+	14	χ2	Z			85%	1	1.4	ATLAS representation, reseeded
G2(3)	64	o	128	χ3+χ4	Z			63%	81	77.2	perm rep on 3888 pts, LLL'ed
G2(3)	78	+	78	χ5	Z			88%	6	26.3	perm rep on 702 pts
G2(3)	91	+	91(a)	χ6	Z			89%	6	35.4	perm rep on 728 pts - LLL'ed
			91(b)	χ7	Z			92%	5	35.0	perm rep on 364 pts
			91(c)	χ8	Z			93%	5	35.0	perm rep on 364b pts
G2(3)	104	+	104	χ9	Z			91%	4	46.0	perm rep on 378b pts, LLL'ed
G2(3)	168	+	168	χ10	Z			87%	26	120.5	perm rep on 351 pts
G2(3)	182	+	182(a)	χ11	Z			85%	2853	151.9	perm rep on 351b pts
			182(b)	χ12	Z			91%	21	139.3	perm rep on 351a pts
3.G2(3)	27	o	No representations available
3.G2(3)	189	o	No representations available

Last generated on Sat Sep 24 18:52:53 2005