Generators and Representations for G = HS

Standard generators

• Standard generators of the Higman-Sims group HS are a and b where a is in class 2A, b is in class 5A and ab has order 11. (Source: ATLAS)
• Standard generators of the double cover 2.HS are preimages A and B where B has order 5 and AB has order 11. (Source: ATLAS)
• Standard generators of the automorphism group HS:2 are c and d where c is in class 2C, d is in class 5C and cd has order 30. (Source: ATLAS)

BBOX programs

• Finder for HS
• Finder for HS.2
• Checker for HS
• Checker for HS.2
• CCL rep tester for HS

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
HS	22	+	22	χ2	Z			86%	2	2.5	perm rep on 100 pts
HS	77	+	77	χ3	Z			91%	4	25.3	perm rep on 100 pts
HS	154	+	154(a)	χ4	Z			61%	355	119.1	perm rep on 1100 pts, cosets of S8
			154(b)	χ5	Z			96%	3	98.3	perm rep on 352 pts
			154(c)	χ6	Z			96%	3	98.3	perm rep on 352 pts
HS	175	+	175	χ7	Z			99%	1	126.4	perm rep on 176 pts
HS	231	+	231	χ8	Z			97%	3	221.1	exterior square of 22-dim
2.HS	56	+	No representations available
2.HS	176	o	No representations available

Last generated on Sat Sep 24 18:52:38 2005