Generators and Representations for G = U₃(4)

Standard generators

• Standard generators of U₃(4) are a and b where a has order 2, b has order 3 and ab has order 13. (Source: ATLAS)

BBOX programs

• Checker for U₃(4)
• CCL rep tester for U₃(4)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
U3(4)	12	-	12	χ2	C			81%		3.4	REPSN package by Dabbaghian-Abdoly, reseeded by E(13)-eigenvector of ab
U3(4)	13	o	13(a)	χ3	C			82%		1.6	perm rep on 325 pts - might be χ4, χ5 or χ6
			13(b)	χ4	C			82%		1.6	Galois conjugate of χ2
			13(c)	χ5	C			82%		1.6	Galois conjugate of χ2
			13(d)	χ6	C			82%		1.6	Galois conjugate of χ2
U3(4)	39	+	39(a)	χ7	C			84%		12.0	perm rep on 208 pts
			39(b)	χ8	C			84%		12.0	Galois conjugate of χ7
U3(4)	52	o	52(a)	χ9	C			93%		16.4	perm rep on 325 pts - got rid of denominator
			52(b)	χ10	C			93%		16.4	Galois conjugate of χ9
			52(c)	χ11	C			93%		16.3	Galois conjugate of χ9
			52(d)	χ12	C			93%		16.3	Galois conjugate of χ9
U3(4)	64	+	64	χ13	Z			97%	1	17.3	perm rep on 65 pts
U3(4)	65	+	65(a)	χ14	Z			73%	7	19.0	perm rep on 208 pts
U3(4)	65	o	260	χ15+χ16+χ17+χ18	Z			59%	44860	436.2	perm rep on 1040 pts
U3(4)	75	o	300	χ19+χ20+χ21+χ22	Z			88%	59	383.8	perm rep on 832 pts

Notes

We assume xy²xy²xy²xyxy is in class 15A. This means its cube is in 5D.

Last generated on Sat Sep 24 18:53:06 2005