Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for HN

Name:

HN

Group order:

273030912000000 = 2¹⁴ ⋅ 3⁶ ⋅ 5⁶ ⋅ 7 ⋅ 11 ⋅ 19

Number of classes:

54

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19]

Maximal subgroups:

	Order	Index	Structure	Name
1	239500800	1140000	A12	A12
2	177408000	1539000	2.HS.2	2.HS.2
3	16547328	16500000	U3(8).31	U3(8).3_1
4	3686400	74064375	21+8.(A5 × A5).2	2^(1+8).(A5xA5).2
5	2520000	108345600	(D10 × U3(5)).2	(D10xU3(5)).2
6	2000000	136515456	51+4:21+4.5.4	5^(1+4):2^(1+4).5.4
7	1658880	164587500	26.U4(2)	2^6.U4(2)
8	1036800	263340000	(A6 × A6).D8	(A6xA6).D8
9	1032192	264515625	23.22.26.(3 × L3(2))	2^3.2^2.2^6.(3xL3(2))
10	750000	364041216	52.5.52.4A5	5^2.5.5^2.4A5
11	190080	1436400000	M12.2	M12.2
12	190080	1436400000	M12.2	HNM12
13	93312	2926000000	34:2(A4 × A4).4	3^4:2(A4xA4).4
14	58320	4681600000	31+4:4A5	3^(1+4):4A5

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	49152	5554828125	HNN2	HNN2
3	5832	46816000000	HNN3	HNN3
5	125000	2184247296	HNN5	HNN5
7	2520	108345600000	(7:3 × A5):2	(7:3xA5):2
11	220	1241049600000	2 × 11:10	2x11:10
19	171	1596672000000	19:9	19:9

Available Brauer tables:

p
2	dec. matrix (PDF)
3	dec. matrix (PDF)
5	dec. matrix (PDF)
7	dec. matrix (PDF)
11	dec. matrix (PDF)
19	dec. matrix (PDF)

Atlas representations:

24 available

Group constructions in GAP:

AtlasGroup( "HN" ), AtlasSubgroup( "HN.2", 1 )

Stored class fusions from this table:

HN.2

Stored class fusions to this table:

2.HS.2, 2³.2².2⁶.(3 × L₃(2)), 2⁶.U₄(2), 2¹⁺⁸.(A₅ × A₅).2, 2¹⁺⁸₊.(2 × A₅), 2¹⁺⁸₊.(A₄ × A₄).2, 2¹⁺⁸₊.(A₄ × A₅), 2^2+1+2+4+2.(3 × S₄), 2 × 11:10, 3⁴.(3 × SL(2, 3)).2, 3⁴:2(A₄ × A₄).4, 3¹⁺⁴:4A₅, 5².5.5².4A₅, 5¹⁺⁴:2¹⁺⁴.5.4, 19:9, (7:3 × A₅):2, (A₆ × A₆).D₈, (A₆ × A₆):2², (A₈ × A₄):2, (A₉ × 3):2, (D₈ × A₆).2², (D₁₀ × U₃(5)).2, (D₁₀ × U₃(5)N2).2, A₁₂, M₁₂.2, HNN2, HNN3, HNN5, M₁₂.2, NDG(2.HS, Q₈).2, NDG(HN, 3²), U₃(8).3₁

File created automatically by GAP on 13-Mar-2024.