Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for 3.A₇

Name:

3.A7

Group order:

7560 = 2³ ⋅ 3³ ⋅ 5 ⋅ 7

Number of classes:

23

InfoText value:

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

Duplicates:

3.U3(5)M2, 3.U3(5)M3

Maximal subgroups:

	Order	Index	Structure	Name
1	1080	7	3.A6	3.A6
2	504	15	3 × L3(2)	3xL3(2)
3	504	15	3 × L3(2)	3xL3(2)
4	360	21	3 × A5.2	3xA5.2
5	216	35	3.(A4 × 3):2	3.(A4x3):2

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	24	315	3 × D8	3xD8
3	108	70	31+2:4	3^(1+2):4
5	60	126	5:4 × 3	5:4x3
7	63	120	7:3 × 3	7:3x3

Available Brauer tables:

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

Atlas representations:

34 available

Group constructions in GAP:

AtlasGroup( "3.A7" ), AtlasSubgroup( "3.M22", 3 ), AtlasSubgroup( "3.M22", 4 ), AtlasSubgroup( "3.ON", 12 ), AtlasSubgroup( "3.ON", 13 ), AtlasSubgroup( "3.Suz", 17 ), PerfectGroup( 7560, 1 )

Stored class fusions from this table:

3.A₇.2, 3.M₂₂, 3.ON, 3.Suz, 3.U₃(5), A₇

Stored class fusions to this table:

2.(2 × 3.A₇), 3.2⁴:A₇, 3.(A₄ × 3):2, 3.A₆, 3.2⁴:A₇, 3¹⁺²:4, 3 × A₅.2, 3 × D₈, 3 × L₃(2), 3 × S₄, 5:4 × 3, 6.A₇, 7:3 × 3

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