Data for HS

Multiplicity-Free Endomorphism Rings

Data for HS

HS

n	U	rank	degree	permutation character	PDF	sources	generators
1	M₂₂	3	100	1a + 22a + 77a	PDF	[PS97], [TomLib]	1, 2
2	U₃(5).2	2	176	1a + 175a	PDF	[PS97], [TomLib]	1, 2
3	U₃(5) < U₃(5).2	4	352	1a + 22a + 154b + 175a	PDF	[PS97], [TomLib]	1, 2
4	U₃(5).2	2	176	1a + 175a	PDF	[PS97], [TomLib]	1, 2
5	U₃(5) < U₃(5).2	4	352	1a + 22a + 154c + 175a	PDF	[PS97], [TomLib]	1, 2
6	L₃(4).2₁	5	1100	1a + 22a + 77a + 175a + 825a	PDF	[PS97], [TomLib]	1, 2
7	A₈.2	5	1100	1a + 77a + 154a + 175a + 693a	PDF	[PS97], [TomLib]	1, 2
8	A₈ < A₈.2	9	2200	1a + 22a + 77a + 154abc + 175a + 693a + 770a	PDF	[Hoe01], [TomLib]	1, 2
9	4³:L₃(2)	9	4125	1a + 22a + 77a + 154a + 175a + 693a + 770a + 825a + 1408a	PDF	[Hoe01], [TomLib]	1, 2
10	M₁₁	9	5600	1a + 22a + 77a + 154b + 175a + 770a + 825a + 1056a + 2520a	PDF	[Hoe01], [TomLib]	1, 2
11	M₁₁	9	5600	1a + 22a + 77a + 154c + 175a + 770a + 825a + 1056a + 2520a	PDF	[Hoe01], [TomLib]	1, 2
12	4.2⁴:S₅	9	5775	1a + 77a + 154a + 175a + 693a + 825a + 1056a + 1386a + 1408a	PDF	[Hoe01], [TomLib]	1, 2

HS.2

n	U	rank	degree	permutation character	PDF	sources	generators
1	M₂₂.2	3	100	1a⁺ + 22a⁺ + 77a⁺	PDF	[PS97]	1, 2
2	M₂₂ < M₂₂.2	6	200	1a^± + 22a^± + 77a^±	PDF	[Hoe01]	1, 2
3	U₃(5).2 < HS	4	352	1a^± + 175a^±	PDF	[PS97]	1, 2
4	U₃(5) < U₃(5).2	7	704	1a^± + 22a^± + 154bc + 175a^±	PDF	[Hoe01]	1, 2
5	5¹⁺²_⁺:[2⁵]	15	22176	1a⁺ + 175a^± + 693a⁺ + 825a⁺ + 896ab + 1056a⁺ + 1386a^- + 1408a⁺ + 1750a^- + 1925a^- + 2520a^± + 2750a^- + 3200a^-	PDF	[Hoe01]	1, 2
6	L₃(4).2²	5	1100	1a⁺ + 22a⁺ + 77a⁺ + 175a⁺ + 825a⁺	PDF	[PS97]	1, 2
7	L₃(4).2₃ < L₃(4).2²	9	2200	1a⁺ + 22a^± + 77a^± + 175a⁺ + 231a^- + 770a^- + 825a⁺	PDF	[Hoe01]	1, 2
8	L₃(4).2₁ < L₃(4).2²	10	2200	1a^± + 22a^± + 77a^± + 175a^± + 825a^±	PDF	[Hoe01]	1, 2
9	A₈.2 × 2	5	1100	1a⁺ + 77a⁺ + 154a⁺ + 175a⁺ + 693a⁺	PDF	[PS97]	1, 2
10	A₈ × 2 < A₈.2 × 2	8	2200	1a⁺ + 22a⁺ + 77a⁺ + 154a⁺bc + 175a⁺ + 693a⁺ + 770a⁺	PDF	[Hoe01]	1, 2
11	A₈.2 < A₈.2 × 2	8	2200	1a⁺ + 22a^- + 77a⁺ + 154a⁺bc + 175a⁺ + 693a⁺ + 770a^-	PDF	[Hoe01]	1, 2
12	A₈.2 < A₈.2 × 2	10	2200	1a^± + 77a^± + 154a^± + 175a^± + 693a^±	PDF	[Hoe01]	1, 2
13	4³:(L₃(2) × 2)	9	4125	1a⁺ + 22a⁺ + 77a⁺ + 154a⁺ + 175a⁺ + 693a⁺ + 770a⁺ + 825a⁺ + 1408a⁺	PDF	[Hoe01]	1, 2
14	4³:L₃(2) < 4³:(L₃(2) × 2)	18	8250	1a^± + 22a^± + 77a^± + 154a^± + 175a^± + 693a^± + 770a^± + 825a^± + 1408a^±	PDF	[Hoe01]	1, 2
15	M₁₁ < HS	17	11200	1a^± + 22a^± + 77a^± + 154bc + 175a^± + 770a^± + 825a^± + 1056a^± + 2520a^±	PDF	[Hoe01]	1, 2
16	2¹⁺⁶_⁺:S₅	9	5775	1a⁺ + 77a⁺ + 154a⁺ + 175a⁺ + 693a⁺ + 825a⁺ + 1056a⁺ + 1386a^- + 1408a⁺	PDF	[Hoe01]	1, 2
17	4.2⁴:S₅ < 2¹⁺⁶_⁺:S₅	18	11550	1a^± + 77a^± + 154a^± + 175a^± + 693a^± + 825a^± + 1056a^± + 1386a^± + 1408a^±	PDF	[Hoe01]	1, 2

2.HS

n	U	rank	degree	permutation character	PDF	sources	generators
1	U₃(5) → (HS,3)	6	704	1a + 22a + 154b + 175a + 176ab	PDF	[Linton]	1, 2
2	U₃(5) → (HS,5)	6	704	1a + 22a + 154c + 175a + 176ab	PDF	[Linton]	1, 2
3	A₈ → (HS,8)	13	4400	1a + 22a + 77a + 154abc + 175a + 176ab + 693a + 770a + 924ab	PDF	[Linton]	1, 2
4	M₁₁ → (HS,10)	16	11200	1a + 22a + 56a + 77a + 154b + 175a + 176ab + 616ab + 770a + 825a + 1056a + 1980ab + 2520a	PDF	[Linton]	1, 2
5	M₁₁ → (HS,11)	16	11200	1a + 22a + 56a + 77a + 154c + 175a + 176ab + 616ab + 770a + 825a + 1056a + 1980ab + 2520a	PDF	[Linton]	1, 2

2.HS.2

n	U	rank	degree	permutation character	PDF	sources	generators
1	A₈ × 2 → (HS.2,10)	10	4400	1a⁺ + 22a⁺ + 77a⁺ + 154a⁺bc + 175a⁺ + 176ab + 693a⁺ + 770a⁺ + 924ab	PDF	[Mue08b]	1, 2
2	A₈.2 → (HS.2,11)	10	4400	1a⁺ + 22a^- + 77a⁺ + 154a⁺bc + 175a⁺ + 176ab + 693a⁺ + 770a^- + 924ab	PDF	[Mue08b]	1, 2

[ATLAS page on HS]

File created automatically by GAP on 23-Jul-2009.