Generators and Representations for G = O₇(3)

Standard generators

• Standard generators of O₇(3) are a and b where a is in class 2A, b has order 7, ab has order 13 and abb has order 20. (Source: ATLAS)
• Standard generators of the double cover 2.O₇(3) are preimages A and B where B has order 7 and AB has order 13. (Source: ATLAS)
• Standard generators of the triple cover 3.O₇(3) are preimages A and B where A has order 2 and B has order 7. (Source: ATLAS)
• Standard generators of the sextuple cover 6.O₇(3) are preimages A and B where A has order 4, B has order 7, and AB has order 39. (Source: ATLAS)

BBOX programs

• Checker for O₇(3)
• CCL rep tester for O₇(3)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
O7(3)	78	+	78	χ2	Z			95%	3	25.9	perm rep on 702 pts
O7(3)	91	+	91	χ3	Z			75%	10	36.6	perm rep on 728 pts - LLL'ed
O7(3)	105	+	105	χ4	Z			90%	4	47.1	perm rep on 1120 pts, LLL'ed
O7(3)	168	+	168	χ5	Z			85%	41	121.3	perm rep on 351 pts - LLL'ed
O7(3)	182	+	182	χ6	Z			92%	31	139.2	perm rep on 351 pts - integerised
O7(3)	195	+	195	χ7	Z			85%	27	163.2	perm rep on 364 pts - LLL'ed
3.O7(3)	27	o	No representations available

Last generated on Sat Sep 24 18:53:13 2005