Generators and Representations for G = L₂(32)

Standard generators

Standard generators of L₂(32) are a and b where a has order 2, b has order 3 and ab is in class 31A/B/C/D/E. The last condition is equivalent to saying that ab has order 31 and ababb has order 11. (Source: ATLAS)
Standard generators of L₂(32):5 are c and d where c has order 2, d has order 5, cd, cdd, cdcdd, cdcdcdd each have order 15, and cdcdcdcddcdcddcdd has order 11. (Source: ATLAS)

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L₂(32)	31	+	31(a)	χ₂	Z			72%	18	4.6	perm rep on 992 pts
			155	χ₃+χ₄+χ₅+χ₆+χ₇	Z			81%	28	103.4	perm rep on 992 pts
			310	χ₈+χ₉+χ₁₀+χ₁₁+χ₁₂+χ₁₃+χ₁₄+χ₁₅+χ₁₆+χ₁₇	Z			80%	249	129.4	perm rep on 992 pts
L₂(32)	32	+	32	χ₁₈	Z			93%	1	4.6	perm rep on 33 pts
L₂(32)	33	+	33(a)	χ₁₉	C			96%		5.4	induce from Borel
			33(b)	χ₂₀	C			96%		5.4	induce from Borel
			33(c)	χ₂₁	C			96%		5.4	induce from Borel
			33(d)	χ₂₂	C			96%		5.4	induce from Borel
			33(e)	χ₂₃	C			96%		5.4	induce from Borel
			33(f)	χ₂₄	C			96%		5.4	induce from Borel
			33(g)	χ₂₅	C			96%		5.4	induce from Borel
			33(h)	χ₂₆	C			96%		5.4	induce from Borel
			33(i)	χ₂₇	C			96%		5.4	induce from Borel
			33(j)	χ₂₈	C			96%		5.4	induce from Borel
			33(k)	χ₂₉	C			96%		5.4	induce from Borel
			33(l)	χ₃₀	C			96%		5.4	induce from Borel
			33(m)	χ₃₁	C			96%		5.4	induce from Borel
			33(n)	χ₃₂	C			96%		5.4	induce from Borel
			33(o)	χ₃₃	C			96%		5.4	induce from Borel

Last generated on Sat Sep 24 18:53:00 2005