Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for J₂.2

Name:

J2.2

Group order:

1209600 = 2⁸ ⋅ 3³ ⋅ 5² ⋅ 7

Number of classes:

27

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7], constructions: Aut(J2)

Maximal subgroups:

	Order	Index	Structure	Name
1	604800	2	J2	J2
2	12096	100	U3(3).2	U3(3).2
3	4320	280	3.A6.22	3.A6.2^2
4	3840	315	21+4.S5	2^(1+4).S5
5	2304	525	22+4:(S3 × S3)	2^(2+4):(S3xS3)
6	1440	840	(A4 × A5):2	(A4xA5):2
7	1200	1008	(A5 × D10).2	(A5xD10).2
8	672	1800	L3(2).2 × 2	L3(2).2x2
9	600	2016	52:(4 × S3)	5^2:(4xS3)
10	120	10080	S5	A5.2

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
3	432	2800	31+2:SD16	3^(1+2):SD16
5	600	2016	52:(4 × S3)	5^2:(4xS3)

Available Brauer tables:

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

Atlas representations:

54 available

Group constructions in GAP:

AtlasGroup( "J2.2" ), AtlasStabilizer( "G2(4).2", "G24d2G1-p416B0" ), AtlasStabilizer( "Suz", "SuzG1-p370656B0" ), AtlasSubgroup( "Suz", 6 ), AutomorphismGroup( AtlasGroup( "J2" ) ), PrimitiveGroup( 100, 2 ), PrimitiveGroup( 280, 22 ), PrimitiveGroup( 315, 3 ), PrimitiveGroup( 525, 6 ), PrimitiveGroup( 840, 4 ), PrimitiveGroup( 1008, 2 ), PrimitiveGroup( 1800, 2 ), PrimitiveGroup( 2016, 5 )

Stored class fusions from this table:

G₂(4).2, J₂.2 × 2, Suz

Stored class fusions to this table:

2.J₂.2, 2¹⁺⁴.S₅, 2²⁺⁴.(S₃ × 2), 2²⁺⁴:(S₃ × S₃), 3.A₆.2², 3¹⁺²:SD₁₆, 5²:(4 × S₃), 5¹⁺⁶:2.J₂.4, (A₄ × A₅):2, (A₅ × D₁₀).2, (A₅ × J₂):2, (D₁₀ × J₂).2, S₅, Isoclinic(2.J₂.2), J₂, L₃(2).2 × 2, S₄ × S₃, U₃(3).2

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