Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for S₇

Name:

A7.2

Group order:

5040 = 2⁴ ⋅ 3² ⋅ 5 ⋅ 7

Number of classes:

15

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7], constructions: Aut(A7)

Maximal subgroups:

	Order	Index	Structure	Name
1	2520	2	A7	A7
2	720	7	S6	A6.2_1
3	240	21	2 × S5	2xS5
4	144	35	S4 × S3	S4xS3
5	42	120	7:6	7:6

Available Brauer tables:

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

Atlas representations:

25 available

Group constructions in GAP:

AtlasGroup( "A7.2" ), AtlasStabilizer( "A8.2", "S8G1-p8B0" ), AtlasStabilizer( "A9", "A9G1-p36B0" ), AtlasStabilizer( "U3(5).2", "U35d2G1-p50B0" ), AtlasSubgroup( "Suz.2", 16 ), AtlasSubgroup( "U3(5).2", 2 ), AutomorphismGroup( AlternatingGroup( 7 ) ), PrimitiveGroup( 7, 7 ), PrimitiveGroup( 21, 3 ), PrimitiveGroup( 35, 4 ), PrimitiveGroup( 120, 1 ), SymmetricGroup( 7 ), TransitiveGroup( 7, 7 ), TransitiveGroup( 14, 46 ), TransitiveGroup( 21, 38 ), TransitiveGroup( 30, 565 )

Stored class fusions from this table:

S₈, A₉, Suz.2, U₃(5).2

Stored class fusions to this table:

2.A₇.2, 2⁶:S₇, 2 × 5:4, 2 × S₅, 2 × S₄, 3.A₇.2, 6.A₇.2, 7:6, (2.A₇ × 3).2, (7:3 × A₇):2, (A₇ × 3):2, (A₇ × (A₅ × A₅):2²):2, (A₇ × A₄):2, (A₇ × A₅):2, (A₇ × A₆):2, (A₇ × L₂(7)):2, S₆, A₇, D₈ × 2, Isoclinic(2.A₇.2), Isoclinic(6.A₇.2), S₄ × S₃, 3²:D₈

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