Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for A₇

Name:

A7

Group order:

2520 = 2³ ⋅ 3² ⋅ 5 ⋅ 7

Number of classes:

9

InfoText value:

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

Duplicates:

U3(5)M2, U3(5)M3, U4(3)M12

Maximal subgroups:

	Order	Index	Structure	Name
1	360	7	A6	A6
2	168	15	L3(2)	L3(2)
3	168	15	L3(2)	L3(2)
4	120	21	S5	A5.2
5	72	35	(A4 × 3):2	(A4x3):2

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	8	315	D8	D8
3	36	70	32:4	3^2:4
5	20	126	5:4	5:4
7	21	120	7:3	7:3

Available Brauer tables:

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

Atlas representations:

33 available

Group constructions in GAP:

AlternatingGroup( 7 ), AtlasGroup( "A7" ), AtlasStabilizer( "A8", "A8G1-p8B0" ), AtlasStabilizer( "M22", "M22G1-p176aB0" ), AtlasStabilizer( "M22", "M22G1-p176bB0" ), AtlasStabilizer( "U3(5)", "U35G1-p50B0" ), AtlasSubgroup( "A7.2", 1 ), AtlasSubgroup( "M22", 3 ), AtlasSubgroup( "M22", 4 ), AtlasSubgroup( "ON", 12 ), AtlasSubgroup( "ON", 13 ), AtlasSubgroup( "Suz", 17 ), PerfectGroup( 2520, 1 ), PrimitiveGroup( 7, 6 ), PrimitiveGroup( 15, 1 ), PrimitiveGroup( 21, 2 ), PrimitiveGroup( 35, 3 ), TransitiveGroup( 7, 6 ), TransitiveGroup( 15, 47 ), TransitiveGroup( 21, 33 )

Stored class fusions from this table:

2⁴:A₇, 2⁶:A₇, S₇, A₈, M₂₂, ON, Suz, U₃(5), U₄(3)

Stored class fusions to this table:

2.(2 × A₇), 2.A₇, 2⁴:A₇, 2⁶:A₇, 3.A₇, 3²:4, 5:4, 6.A₇, 7:3, (A₄ × 3):2, S₅, A₆, D₈, L₃(2), 2⁴:A₇, P27/G1/L1/V1/ext2, P27/G1/L1/V1/ext3, P27/G1/L1/V1/ext4, S₄

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