Generators and Representations for G = O₈⁺(2)

Standard generators

• Standard generators of O₈⁺(2) are a and b where a is in class 2E, b is in class 5A, ab is in class 12F (or 12G) and ababababbababbabb has order 8. (Source: ATLAS)
• Standard generators of the double cover 2.O₈⁺(2) are preimages A and B where B has order 5, ABB has order 15 and B is in class +5A. (Source: ATLAS)

BBOX programs

• Checker for O₈⁺(2)
• CCL rep tester for O₈⁺(2)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
O8+(2)	28	+	28	χ2	Z			90%	1	3.8	exterior square of Weyl group rep
O8+(2)	35	+	35(a)	χ3	Z			84%	3	5.9	perm rep on 120a pts
			35(b)	χ4	Z			91%	1	5.8	perm rep on 120c pts
			35(c)	χ5	Z			88%	2	5.8	perm rep on 120b pts
O8+(2)	50	+	50	χ6	Z			93%	2	11.0	perm rep on 135 pts
O8+(2)	84	+	84(a)	χ7	Z			94%	3	29.9	perm rep on 120a pts
			84(b)	χ8	Z			95%	3	29.9	perm rep on 120c pts
			84(c)	χ9	Z			93%	3	30.0	perm rep on 120b pts
O8+(2)	175	+	175	χ10	Z			69%	120	141.3	perm rep on 960 pts, LLL'ed
O8+(2)	210	+	210(a)	χ11	Z			73%	158	201.4	perm rep on 1080a pts
			210(b)	χ12	Z			68%	105	207.2	perm rep on 1080c pts
			210(c)	χ13	Z			68%	98	205.3	perm rep on 1080b pts
2.O8+(2)	8	+	No representations available
2.O8+(2)	56	+	No representations available
2.O8+(2)	112	+	No representations available
2.O8+(2)	160	+	No representations available
2.O8+(2)	224	+	No representations available

Last generated on Sat Sep 24 18:53:14 2005