Generators and Representations for G = Sz(8)

Standard generators

• Standard generators of Sz(8) are a and b where a has order 2, b has order 4, ab has order 5, abb has order 7 and ababbbabb has order 7. The condition that abb has order 7 is redundant. (Source: ATLAS)
• Standard generators of a particular double cover 2.Sz(8) are preimages A and B where AB has order 5, ABB has order 7 and ABABBBABB has order 7. Note that if (a, b) is fixed, then these relations only hold in one of the three double covers. (Source: ATLAS)

BBOX programs

• Checker for Sz(8)
• CCL rep tester for Sz(8)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
Sz(8)	14	o	14(a)	χ2	Z(i)			65%		1.6	complex conjugate of χ3
			14(b)	χ3	Z(i)			65%		1.6
Sz(8)	35	+	105	χ4+χ5+χ6	Z(i)			83%		57.1
Sz(8)	64	+	64	χ7	Z			96%	1	17.4	right gens this time
Sz(8)	65	+	65(a)	χ8	C			98%		17.9	Galois conjugate of χ10
			65(b)	χ9	C			98%		17.9	Galois conjugate of χ10
			65(c)	χ10	C			98%		18.6	Use transvection {1, uw : u in U} for W = the Weyl group
Sz(8)	91	+	91	χ11	Z			61%	29	38.2	only fairly nasty
2.Sz(8)	40	+	No representations available
2.Sz(8)	56	+	No representations available
2.Sz(8)	64	+	No representations available
2.Sz(8)	104	+	No representations available

Notes

y is in 4A, xyxy² is in 7A.

Last generated on Sat Sep 24 18:52:54 2005