Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for 2.HS.2

Name:

2.HS.2

Group order:

177408000 = 2¹¹ ⋅ 3² ⋅ 5³ ⋅ 7 ⋅ 11

Number of classes:

57

InfoText value:

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

Some maximal subgroups:

	Order	Index	Structure	Name
1	88704000	2	2.HS	2.HS
2	1774080	100	2.M22.2	2.M22.2
3	161280	1100	2.L3(4).(22)1*23	2.L3(4).(2^2)_{1*23}
9	8000	22176	51+2+:[26]	2.HS.2N5

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	2048	86625	2.HS.2N2	2.HS.2N2
3	1152	154000	2.HS.2N3	2.HS.2N3
5	8000	22176	51+2+:[26]	2.HS.2N5

Available Brauer tables:

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

Atlas representations:

6 available

Group constructions in GAP:

AtlasGroup( "2.HS.2" ), AtlasStabilizer( "HN", "HNG1-p1539000B0" ), AtlasSubgroup( "HN", 2 )

Stored class fusions from this table:

4.HS.2, HN, HS.2

Stored class fusions to this table:

2.HS, 2.HS.2N2, 2.HS.2N3, 5¹⁺²₊:[2⁶], 2.L₃(4).(2²)_1*23, 2.M₂₂.2, 2 × 11:10, NDG(2.HS, Q₈).2

File created automatically by GAP on 20-May-2025.