Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for HN.2

Name:

HN.2

Group order:

546061824000000 = 2¹⁵ ⋅ 3⁶ ⋅ 5⁶ ⋅ 7 ⋅ 11 ⋅ 19

Number of classes:

78

InfoText value:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	273030912000000	2	HN	HN
2	479001600	1140000	S12	A12.2
3	354816000	1539000	4.HS.2	4.HS.2
4	33094656	16500000	U3(8).6	U3(8).6
5	7372800	74064375	21+8+.(A5 × A5).22	2^(1+8)_+.(A5xA5).2^2
6	5040000	108345600	5:4 × U3(5):2	5:4xU3(5):2
7	4000000	136515456	51+4+:(4Y21+4−.5.4)	5^(1+4)_+:(4Y2^(1+4)_-.5.4)
8	3317760	164587500	26.U4(2).2	2^6.U4(2).2
9	2073600	263340000	(S6 × S6).22	(S6xS6).2^2
10	2064384	264515625	23.22.26.(S3 × L3(2))	2^3.2^2.2^6.(S3xL3(2))
11	1500000	364041216	52.5.52.4S5	5^2.5.5^2.4S5
12	186624	2926000000	34:2(S4 × S4).2	3^4:2(S4xS4).2
13	116640	4681600000	31+4+:4S5	HN.2M13

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
3	11664	46816000000	HN.2N3	HN.2N3
5	250000	2184247296	LyN5	LyN5

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:

8 available

Group constructions in GAP:

AtlasGroup( "HN.2" ), AtlasSubgroup( "B", 11 ), AutomorphismGroup( AtlasGroup( "HN" ) )

Stored class fusions from this table:

B

Stored class fusions to this table:

2³.2².2⁶.(S₃ × L₃(2)), 2⁶.U₄(2).2, 2¹⁺⁸₊.(A₅ × A₅).2², 3⁴:2(S₄ × S₄).2, 4.HS.2, 5:4 × U₃(5).2N2, 5:4 × U₃(5):2, 5².5.5².4S₅, 5¹⁺⁴₊:(4Y₂¹⁺⁴₋.5.4), 19:18, (D₁₀ × HN).2, (S₆ × S₆).2², S₁₂, HN, 3¹⁺⁴₊:4S₅, HN.2N3, LyN5, NDG(HN.2, 3²), S₈ × S₄, S₉ × S₃, U₃(8).6

File created automatically by GAP on 6-May-2025.